Complex Dynamics of a Predator-Prey System With Gompertz Growth and Herd Behavior

The complex dynamics of a predator-prey system in discrete time are studied. In this system, we consider the prey’s Gompertz growth and the square-root functional response. The existence of fixed points and stability are examined. Using the center manifold and bifurcation theory, we found that the s...
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Autor*in:	Rizwan Ahmed [verfasserIn] M. B. Almatrafi [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Übergeordnetes Werk:	In: International Journal of Analysis and Applications - Etamaths Publishing, 2013, 21(2023), Seite 100-100
Übergeordnetes Werk:	volume:21 ; year:2023 ; pages:100-100

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.28924/2291-8639-21-2023-100

Katalog-ID:	DOAJ100151035

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520			\|a The complex dynamics of a predator-prey system in discrete time are studied. In this system, we consider the prey’s Gompertz growth and the square-root functional response. The existence of fixed points and stability are examined. Using the center manifold and bifurcation theory, we found that the system undergoes transcritical bifurcation, period-doubling bifurcation, and Neimark-Sacker bifurcation. In addition, numerical examples are presented to illustrate the consistency of the analytical findings. The bifurcation diagrams show that the positive fixed point is stable if the death rate of the predator is greater than a threshold value. Biologically, it means that to prevent the predator population from growing uncontrollably and stability of the positive fixed point, the predator’s death rate should be greater than the threshold value.
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allfieldsSound	10.28924/2291-8639-21-2023-100 doi (DE-627)DOAJ100151035 (DE-599)DOAJdffea1f670f54ac8ade1cbb4c37be5f8 DE-627 ger DE-627 rakwb eng QA273-280 QA299.6-433 Rizwan Ahmed verfasserin aut Complex Dynamics of a Predator-Prey System With Gompertz Growth and Herd Behavior 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The complex dynamics of a predator-prey system in discrete time are studied. In this system, we consider the prey’s Gompertz growth and the square-root functional response. The existence of fixed points and stability are examined. Using the center manifold and bifurcation theory, we found that the system undergoes transcritical bifurcation, period-doubling bifurcation, and Neimark-Sacker bifurcation. In addition, numerical examples are presented to illustrate the consistency of the analytical findings. The bifurcation diagrams show that the positive fixed point is stable if the death rate of the predator is greater than a threshold value. Biologically, it means that to prevent the predator population from growing uncontrollably and stability of the positive fixed point, the predator’s death rate should be greater than the threshold value. Probabilities. Mathematical statistics Analysis M. B. Almatrafi verfasserin aut In International Journal of Analysis and Applications Etamaths Publishing, 2013 21(2023), Seite 100-100 (DE-627)768577276 (DE-600)2733853-8 22918639 nnns volume:21 year:2023 pages:100-100 https://doi.org/10.28924/2291-8639-21-2023-100 kostenfrei https://doaj.org/article/dffea1f670f54ac8ade1cbb4c37be5f8 kostenfrei http://etamaths.com/index.php/ijaa/article/view/2910 kostenfrei https://doaj.org/toc/2291-8639 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 21 2023 100-100
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source	In International Journal of Analysis and Applications 21(2023), Seite 100-100 volume:21 year:2023 pages:100-100
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callnumber-first	Q - Science
author	Rizwan Ahmed
spellingShingle	Rizwan Ahmed misc QA273-280 misc QA299.6-433 misc Probabilities. Mathematical statistics misc Analysis Complex Dynamics of a Predator-Prey System With Gompertz Growth and Herd Behavior
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topic_title	QA273-280 QA299.6-433 Complex Dynamics of a Predator-Prey System With Gompertz Growth and Herd Behavior
topic	misc QA273-280 misc QA299.6-433 misc Probabilities. Mathematical statistics misc Analysis
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title	Complex Dynamics of a Predator-Prey System With Gompertz Growth and Herd Behavior
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title_full	Complex Dynamics of a Predator-Prey System With Gompertz Growth and Herd Behavior
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title_sort	complex dynamics of a predator-prey system with gompertz growth and herd behavior
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title_auth	Complex Dynamics of a Predator-Prey System With Gompertz Growth and Herd Behavior
abstract	The complex dynamics of a predator-prey system in discrete time are studied. In this system, we consider the prey’s Gompertz growth and the square-root functional response. The existence of fixed points and stability are examined. Using the center manifold and bifurcation theory, we found that the system undergoes transcritical bifurcation, period-doubling bifurcation, and Neimark-Sacker bifurcation. In addition, numerical examples are presented to illustrate the consistency of the analytical findings. The bifurcation diagrams show that the positive fixed point is stable if the death rate of the predator is greater than a threshold value. Biologically, it means that to prevent the predator population from growing uncontrollably and stability of the positive fixed point, the predator’s death rate should be greater than the threshold value.
abstractGer	The complex dynamics of a predator-prey system in discrete time are studied. In this system, we consider the prey’s Gompertz growth and the square-root functional response. The existence of fixed points and stability are examined. Using the center manifold and bifurcation theory, we found that the system undergoes transcritical bifurcation, period-doubling bifurcation, and Neimark-Sacker bifurcation. In addition, numerical examples are presented to illustrate the consistency of the analytical findings. The bifurcation diagrams show that the positive fixed point is stable if the death rate of the predator is greater than a threshold value. Biologically, it means that to prevent the predator population from growing uncontrollably and stability of the positive fixed point, the predator’s death rate should be greater than the threshold value.
abstract_unstemmed	The complex dynamics of a predator-prey system in discrete time are studied. In this system, we consider the prey’s Gompertz growth and the square-root functional response. The existence of fixed points and stability are examined. Using the center manifold and bifurcation theory, we found that the system undergoes transcritical bifurcation, period-doubling bifurcation, and Neimark-Sacker bifurcation. In addition, numerical examples are presented to illustrate the consistency of the analytical findings. The bifurcation diagrams show that the positive fixed point is stable if the death rate of the predator is greater than a threshold value. Biologically, it means that to prevent the predator population from growing uncontrollably and stability of the positive fixed point, the predator’s death rate should be greater than the threshold value.
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title_short	Complex Dynamics of a Predator-Prey System With Gompertz Growth and Herd Behavior
url	https://doi.org/10.28924/2291-8639-21-2023-100 https://doaj.org/article/dffea1f670f54ac8ade1cbb4c37be5f8 http://etamaths.com/index.php/ijaa/article/view/2910 https://doaj.org/toc/2291-8639
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