2016
DOI: 10.5539/jmr.v8n3p22
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Hopf-bifurcation Limit Cycles of an Extended Rosenzweig-MacArthur Model

Abstract: <p>In this paper, we formulated a new topologically equivalence dynamics of an Extended Rosenzweig-MacArthur Model. Also, we investigated the local stability criteria, and determine the existence of co-dimension-1 Hopf-bifurcation limit cycles as the bifurcation-parameter changes. We discussed the dynamical complexities of this model using numerical responses, solution curves and phase-space diagrams.</p>

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Cited by 5 publications
(2 citation statements)
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“…where x1(t), x2(t), and x3(t) are the population densities of the interacting species and r, K, a2, a3, b1, b2, c2, c3, d2 and d3 are positive ecological parameters. In [12] a topologically equivalent dynamical model of system (2.1) was obtained via non-dimensionalization of the state variables as follows:…”
Section: Model Formulation and Its Invariance Regionmentioning
confidence: 99%
“…where x1(t), x2(t), and x3(t) are the population densities of the interacting species and r, K, a2, a3, b1, b2, c2, c3, d2 and d3 are positive ecological parameters. In [12] a topologically equivalent dynamical model of system (2.1) was obtained via non-dimensionalization of the state variables as follows:…”
Section: Model Formulation and Its Invariance Regionmentioning
confidence: 99%
“…It is more realistic to assume that the interactions would saturate because of the limiting carrying capacity of the environment. The Rosenzweig-MacArthur models with limited resources attract more and more scholars to study the effect of various factors on prey-predator interactions; see various studies [5,10,20]. This kind of models can be applied to species living in the world's oceans and animal populations on land [3,7,23].…”
Section: Introductionmentioning
confidence: 99%