Stability and bifurcation analysis of a discrete Leslie predator-prey system via piecewise constant argument method

The objective of this study was to analyze the complex dynamics of a discrete-time predator-prey system by using the piecewise constant argument technique. The existence and stability of fixed points were examined. It was shown that the system experienced period-doubling (PD) and Neimark-Sacker (NS)...
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Autor*in:	Saud Fahad Aldosary [verfasserIn] Rizwan Ahmed [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	predator-prey leslie-gower piecewise-constant argument method stability bifurcation chaos control

Übergeordnetes Werk:	In: AIMS Mathematics - AIMS Press, 2018, 9(2024), 2, Seite 4684-4706
Übergeordnetes Werk:	volume:9 ; year:2024 ; number:2 ; pages:4684-4706

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3934/math.2024226

Katalog-ID:	DOAJ09485422X

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callnumber-first	Q - Science
author	Saud Fahad Aldosary
spellingShingle	Saud Fahad Aldosary misc QA1-939 misc predator-prey misc leslie-gower misc piecewise-constant argument method misc stability misc bifurcation misc chaos control misc Mathematics Stability and bifurcation analysis of a discrete Leslie predator-prey system via piecewise constant argument method
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topic_title	QA1-939 Stability and bifurcation analysis of a discrete Leslie predator-prey system via piecewise constant argument method predator-prey leslie-gower piecewise-constant argument method stability bifurcation chaos control
topic	misc QA1-939 misc predator-prey misc leslie-gower misc piecewise-constant argument method misc stability misc bifurcation misc chaos control misc Mathematics
topic_unstemmed	misc QA1-939 misc predator-prey misc leslie-gower misc piecewise-constant argument method misc stability misc bifurcation misc chaos control misc Mathematics
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title	Stability and bifurcation analysis of a discrete Leslie predator-prey system via piecewise constant argument method
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title_full	Stability and bifurcation analysis of a discrete Leslie predator-prey system via piecewise constant argument method
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title_sort	stability and bifurcation analysis of a discrete leslie predator-prey system via piecewise constant argument method
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title_auth	Stability and bifurcation analysis of a discrete Leslie predator-prey system via piecewise constant argument method
abstract	The objective of this study was to analyze the complex dynamics of a discrete-time predator-prey system by using the piecewise constant argument technique. The existence and stability of fixed points were examined. It was shown that the system experienced period-doubling (PD) and Neimark-Sacker (NS) bifurcations at the positive fixed point by using the center manifold and bifurcation theory. The management of the system's bifurcating and fluctuating behavior may be controlled via the use of feedback and hybrid control approaches. Both methods were effective in controlling bifurcation and chaos. Furthermore, we used numerical simulations to empirically validate our theoretical findings. The chaotic behaviors of the system were recognized through bifurcation diagrams and maximum Lyapunov exponent graphs. The stability of the positive fixed point within the optimal prey growth rate range $ A_1 < a < A_2 $ was highlighted by our observations. When the value of $ a $ falls below a certain threshold $ A_1 $, it becomes challenging to effectively sustain prey populations in the face of predation, thereby affecting the survival of predators. When the growth rate surpasses a specific threshold denoted as $ A_2 $, it initiates a phase of rapid expansion. Predators initially benefit from this phase because it supplies them with sufficient food. Subsequently, resource depletion could occur, potentially resulting in long-term consequences for populations of both the predator and prey. Therefore, a moderate amount of prey's growth rate was beneficial for both predator and prey populations.
abstractGer	The objective of this study was to analyze the complex dynamics of a discrete-time predator-prey system by using the piecewise constant argument technique. The existence and stability of fixed points were examined. It was shown that the system experienced period-doubling (PD) and Neimark-Sacker (NS) bifurcations at the positive fixed point by using the center manifold and bifurcation theory. The management of the system's bifurcating and fluctuating behavior may be controlled via the use of feedback and hybrid control approaches. Both methods were effective in controlling bifurcation and chaos. Furthermore, we used numerical simulations to empirically validate our theoretical findings. The chaotic behaviors of the system were recognized through bifurcation diagrams and maximum Lyapunov exponent graphs. The stability of the positive fixed point within the optimal prey growth rate range $ A_1 < a < A_2 $ was highlighted by our observations. When the value of $ a $ falls below a certain threshold $ A_1 $, it becomes challenging to effectively sustain prey populations in the face of predation, thereby affecting the survival of predators. When the growth rate surpasses a specific threshold denoted as $ A_2 $, it initiates a phase of rapid expansion. Predators initially benefit from this phase because it supplies them with sufficient food. Subsequently, resource depletion could occur, potentially resulting in long-term consequences for populations of both the predator and prey. Therefore, a moderate amount of prey's growth rate was beneficial for both predator and prey populations.
abstract_unstemmed	The objective of this study was to analyze the complex dynamics of a discrete-time predator-prey system by using the piecewise constant argument technique. The existence and stability of fixed points were examined. It was shown that the system experienced period-doubling (PD) and Neimark-Sacker (NS) bifurcations at the positive fixed point by using the center manifold and bifurcation theory. The management of the system's bifurcating and fluctuating behavior may be controlled via the use of feedback and hybrid control approaches. Both methods were effective in controlling bifurcation and chaos. Furthermore, we used numerical simulations to empirically validate our theoretical findings. The chaotic behaviors of the system were recognized through bifurcation diagrams and maximum Lyapunov exponent graphs. The stability of the positive fixed point within the optimal prey growth rate range $ A_1 < a < A_2 $ was highlighted by our observations. When the value of $ a $ falls below a certain threshold $ A_1 $, it becomes challenging to effectively sustain prey populations in the face of predation, thereby affecting the survival of predators. When the growth rate surpasses a specific threshold denoted as $ A_2 $, it initiates a phase of rapid expansion. Predators initially benefit from this phase because it supplies them with sufficient food. Subsequently, resource depletion could occur, potentially resulting in long-term consequences for populations of both the predator and prey. Therefore, a moderate amount of prey's growth rate was beneficial for both predator and prey populations.
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title_short	Stability and bifurcation analysis of a discrete Leslie predator-prey system via piecewise constant argument method
url	https://doi.org/10.3934/math.2024226 https://doaj.org/article/230e1c2fad7a443191d422f64526a504 https://www.aimspress.com/article/doi/10.3934/math.2024226?viewType=HTML https://doaj.org/toc/2473-6988
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Stability and bifurcation analysis of a discrete Leslie predator-prey system via piecewise constant argument method

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