Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting
Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Mondal, Bapin [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022transfer abstract |
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| Schlagwörter: |
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| Umfang: |
25 |
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| Übergeordnetes Werk: |
Enthalten in: Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model - Hendawy, Hanan ELSEVIER, 2022, transactions of IMACS, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:192 ; year:2022 ; pages:111-135 ; extent:25 |
| Links: |
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| DOI / URN: |
10.1016/j.matcom.2021.08.019 |
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ELV055651356 |
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| 520 | |a Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. | ||
| 520 | |a Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. | ||
| 650 | 7 | |a Imprecise prey–predator |2 Elsevier | |
| 650 | 7 | |a Saddle–node bifurcation |2 Elsevier | |
| 650 | 7 | |a Bogdanov–Takens bifurcation |2 Elsevier | |
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| 700 | 1 | |a Ghosh, Uttam |4 oth | |
| 700 | 1 | |a Rahman, Md Sadikur |4 oth | |
| 700 | 1 | |a Saha, Pritam |4 oth | |
| 700 | 1 | |a Sarkar, Susmita |4 oth | |
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10.1016/j.matcom.2021.08.019 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001558.pica (DE-627)ELV055651356 (ELSEVIER)S0378-4754(21)00309-8 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Mondal, Bapin verfasserin aut Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting 2022transfer abstract 25 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. Imprecise prey–predator Elsevier Saddle–node bifurcation Elsevier Bogdanov–Takens bifurcation Elsevier Hopf bifurcation Elsevier Ghosh, Uttam oth Rahman, Md Sadikur oth Saha, Pritam oth Sarkar, Susmita oth Enthalten in Elsevier Science Hendawy, Hanan ELSEVIER Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model 2022 transactions of IMACS Amsterdam [u.a.] (DE-627)ELV009822585 volume:192 year:2022 pages:111-135 extent:25 https://doi.org/10.1016/j.matcom.2021.08.019 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 192 2022 111-135 25 |
| spelling |
10.1016/j.matcom.2021.08.019 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001558.pica (DE-627)ELV055651356 (ELSEVIER)S0378-4754(21)00309-8 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Mondal, Bapin verfasserin aut Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting 2022transfer abstract 25 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. Imprecise prey–predator Elsevier Saddle–node bifurcation Elsevier Bogdanov–Takens bifurcation Elsevier Hopf bifurcation Elsevier Ghosh, Uttam oth Rahman, Md Sadikur oth Saha, Pritam oth Sarkar, Susmita oth Enthalten in Elsevier Science Hendawy, Hanan ELSEVIER Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model 2022 transactions of IMACS Amsterdam [u.a.] (DE-627)ELV009822585 volume:192 year:2022 pages:111-135 extent:25 https://doi.org/10.1016/j.matcom.2021.08.019 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 192 2022 111-135 25 |
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10.1016/j.matcom.2021.08.019 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001558.pica (DE-627)ELV055651356 (ELSEVIER)S0378-4754(21)00309-8 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Mondal, Bapin verfasserin aut Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting 2022transfer abstract 25 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. Imprecise prey–predator Elsevier Saddle–node bifurcation Elsevier Bogdanov–Takens bifurcation Elsevier Hopf bifurcation Elsevier Ghosh, Uttam oth Rahman, Md Sadikur oth Saha, Pritam oth Sarkar, Susmita oth Enthalten in Elsevier Science Hendawy, Hanan ELSEVIER Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model 2022 transactions of IMACS Amsterdam [u.a.] (DE-627)ELV009822585 volume:192 year:2022 pages:111-135 extent:25 https://doi.org/10.1016/j.matcom.2021.08.019 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 192 2022 111-135 25 |
| allfieldsGer |
10.1016/j.matcom.2021.08.019 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001558.pica (DE-627)ELV055651356 (ELSEVIER)S0378-4754(21)00309-8 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Mondal, Bapin verfasserin aut Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting 2022transfer abstract 25 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. Imprecise prey–predator Elsevier Saddle–node bifurcation Elsevier Bogdanov–Takens bifurcation Elsevier Hopf bifurcation Elsevier Ghosh, Uttam oth Rahman, Md Sadikur oth Saha, Pritam oth Sarkar, Susmita oth Enthalten in Elsevier Science Hendawy, Hanan ELSEVIER Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model 2022 transactions of IMACS Amsterdam [u.a.] (DE-627)ELV009822585 volume:192 year:2022 pages:111-135 extent:25 https://doi.org/10.1016/j.matcom.2021.08.019 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 192 2022 111-135 25 |
| allfieldsSound |
10.1016/j.matcom.2021.08.019 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001558.pica (DE-627)ELV055651356 (ELSEVIER)S0378-4754(21)00309-8 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Mondal, Bapin verfasserin aut Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting 2022transfer abstract 25 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. Imprecise prey–predator Elsevier Saddle–node bifurcation Elsevier Bogdanov–Takens bifurcation Elsevier Hopf bifurcation Elsevier Ghosh, Uttam oth Rahman, Md Sadikur oth Saha, Pritam oth Sarkar, Susmita oth Enthalten in Elsevier Science Hendawy, Hanan ELSEVIER Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model 2022 transactions of IMACS Amsterdam [u.a.] (DE-627)ELV009822585 volume:192 year:2022 pages:111-135 extent:25 https://doi.org/10.1016/j.matcom.2021.08.019 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 192 2022 111-135 25 |
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Enthalten in Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model Amsterdam [u.a.] volume:192 year:2022 pages:111-135 extent:25 |
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Cultured versus freshly isolated adipose-derived stem cells in improvement of the histopathological outcomes in HCL-induced cystitis in a rat model |
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studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting |
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Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting |
| abstract |
Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. |
| abstractGer |
Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. |
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Study of a food chain model under uncertainty is quite difficult. Because, in an uncertain food chain model, the biological parameters can’t be determined accurately. The aim of this work is to study the stability and local bifurcations (Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation) of an imprecise prey–predator system in an uncertain environment. The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population. To study the proposed imprecise system mathematically, the dynamical interactions between the imprecise species are presented by the system of governing interval differential equations. And to study the dynamics of the proposed imprecise system theoretically, it is modelled in a precise way by the linear parametric representation of the interval. Then all the theoretical analyses, including Saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens (BT) bifurcation of the interior equilibrium point of the proposed imprecise model are discussed in parametric form. To verify all the theoretical analyses of the proposed imprecise model, numerical simulations with interval-valued hypothetical data of the imprecise parameters are performed graphically. Finally, the work is concluded with some biological consequences. |
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Studies of different types of bifurcations analyses of an imprecise two species food chain model with fear effect and non-linear harvesting |
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