Bifurcations in a discrete predator–prey model with nonmonotonic functional response
The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are d...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Huang, Jicai [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2018transfer abstract |
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| Schlagwörter: |
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| Umfang: |
30 |
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| Übergeordnetes Werk: |
Enthalten in: In silico drug repurposing in COVID-19: A network-based analysis - Sibilio, Pasquale ELSEVIER, 2021, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:464 ; year:2018 ; number:1 ; day:1 ; month:08 ; pages:201-230 ; extent:30 |
| Links: |
|---|
| DOI / URN: |
10.1016/j.jmaa.2018.03.074 |
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| 520 | |a The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. | ||
| 520 | |a The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. | ||
| 650 | 7 | |a Neimark–Sacker bifurcation |2 Elsevier | |
| 650 | 7 | |a Discrete predator–prey model |2 Elsevier | |
| 650 | 7 | |a Transcritical bifurcation |2 Elsevier | |
| 650 | 7 | |a Fold bifurcation |2 Elsevier | |
| 650 | 7 | |a Bogdanov–Takens bifurcation |2 Elsevier | |
| 650 | 7 | |a Flip bifurcations |2 Elsevier | |
| 700 | 1 | |a Liu, Sanhong |4 oth | |
| 700 | 1 | |a Ruan, Shigui |4 oth | |
| 700 | 1 | |a Xiao, Dongmei |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n Elsevier |a Sibilio, Pasquale ELSEVIER |t In silico drug repurposing in COVID-19: A network-based analysis |d 2021 |g Amsterdam [u.a.] |w (DE-627)ELV006634001 |
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10.1016/j.jmaa.2018.03.074 doi GBV00000000000486.pica (DE-627)ELV042861276 (ELSEVIER)S0022-247X(18)30286-5 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Huang, Jicai verfasserin aut Bifurcations in a discrete predator–prey model with nonmonotonic functional response 2018transfer abstract 30 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. Neimark–Sacker bifurcation Elsevier Discrete predator–prey model Elsevier Transcritical bifurcation Elsevier Fold bifurcation Elsevier Bogdanov–Takens bifurcation Elsevier Flip bifurcations Elsevier Liu, Sanhong oth Ruan, Shigui oth Xiao, Dongmei oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:464 year:2018 number:1 day:1 month:08 pages:201-230 extent:30 https://doi.org/10.1016/j.jmaa.2018.03.074 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 464 2018 1 1 0801 201-230 30 |
| spelling |
10.1016/j.jmaa.2018.03.074 doi GBV00000000000486.pica (DE-627)ELV042861276 (ELSEVIER)S0022-247X(18)30286-5 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Huang, Jicai verfasserin aut Bifurcations in a discrete predator–prey model with nonmonotonic functional response 2018transfer abstract 30 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. Neimark–Sacker bifurcation Elsevier Discrete predator–prey model Elsevier Transcritical bifurcation Elsevier Fold bifurcation Elsevier Bogdanov–Takens bifurcation Elsevier Flip bifurcations Elsevier Liu, Sanhong oth Ruan, Shigui oth Xiao, Dongmei oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:464 year:2018 number:1 day:1 month:08 pages:201-230 extent:30 https://doi.org/10.1016/j.jmaa.2018.03.074 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 464 2018 1 1 0801 201-230 30 |
| allfields_unstemmed |
10.1016/j.jmaa.2018.03.074 doi GBV00000000000486.pica (DE-627)ELV042861276 (ELSEVIER)S0022-247X(18)30286-5 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Huang, Jicai verfasserin aut Bifurcations in a discrete predator–prey model with nonmonotonic functional response 2018transfer abstract 30 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. Neimark–Sacker bifurcation Elsevier Discrete predator–prey model Elsevier Transcritical bifurcation Elsevier Fold bifurcation Elsevier Bogdanov–Takens bifurcation Elsevier Flip bifurcations Elsevier Liu, Sanhong oth Ruan, Shigui oth Xiao, Dongmei oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:464 year:2018 number:1 day:1 month:08 pages:201-230 extent:30 https://doi.org/10.1016/j.jmaa.2018.03.074 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 464 2018 1 1 0801 201-230 30 |
| allfieldsGer |
10.1016/j.jmaa.2018.03.074 doi GBV00000000000486.pica (DE-627)ELV042861276 (ELSEVIER)S0022-247X(18)30286-5 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Huang, Jicai verfasserin aut Bifurcations in a discrete predator–prey model with nonmonotonic functional response 2018transfer abstract 30 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. Neimark–Sacker bifurcation Elsevier Discrete predator–prey model Elsevier Transcritical bifurcation Elsevier Fold bifurcation Elsevier Bogdanov–Takens bifurcation Elsevier Flip bifurcations Elsevier Liu, Sanhong oth Ruan, Shigui oth Xiao, Dongmei oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:464 year:2018 number:1 day:1 month:08 pages:201-230 extent:30 https://doi.org/10.1016/j.jmaa.2018.03.074 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 464 2018 1 1 0801 201-230 30 |
| allfieldsSound |
10.1016/j.jmaa.2018.03.074 doi GBV00000000000486.pica (DE-627)ELV042861276 (ELSEVIER)S0022-247X(18)30286-5 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Huang, Jicai verfasserin aut Bifurcations in a discrete predator–prey model with nonmonotonic functional response 2018transfer abstract 30 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. Neimark–Sacker bifurcation Elsevier Discrete predator–prey model Elsevier Transcritical bifurcation Elsevier Fold bifurcation Elsevier Bogdanov–Takens bifurcation Elsevier Flip bifurcations Elsevier Liu, Sanhong oth Ruan, Shigui oth Xiao, Dongmei oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:464 year:2018 number:1 day:1 month:08 pages:201-230 extent:30 https://doi.org/10.1016/j.jmaa.2018.03.074 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 464 2018 1 1 0801 201-230 30 |
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Enthalten in In silico drug repurposing in COVID-19: A network-based analysis Amsterdam [u.a.] volume:464 year:2018 number:1 day:1 month:08 pages:201-230 extent:30 |
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Enthalten in In silico drug repurposing in COVID-19: A network-based analysis Amsterdam [u.a.] volume:464 year:2018 number:1 day:1 month:08 pages:201-230 extent:30 |
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Neimark–Sacker bifurcation Discrete predator–prey model Transcritical bifurcation Fold bifurcation Bogdanov–Takens bifurcation Flip bifurcations |
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In silico drug repurposing in COVID-19: A network-based analysis |
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Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. 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It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. 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Bifurcations in a discrete predator–prey model with nonmonotonic functional response |
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The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. |
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The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. |
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The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time. |
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