Complex dynamics in a ratio-dependent two-predator one-prey model

Agrawal, Tanuja; Saleem, Muhammad

doi:10.1007/s40314-014-0115-1

Cited by 12 publications

(8 citation statements)

References 32 publications

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“…In ecology, several authors discussed the dynamics of predator-prey model and contributed to the development of the population dynamics [2,6,13].…”

Section: Stability and Bifurcation: Discrete Differentialmentioning

confidence: 99%

“…We discover the equilibrium positions of the model (2) by calculating the variational matrix of the predator-prey model (2). To determine the equilibrium positions we need to solve the following nonlinear system: Now, we examine the behavior of the model (2) around each of the above equilibrium positions.…”

Section: Equilibrium Positions and Variational Matrix Of Model (2)mentioning

confidence: 99%

“…We investigate the stability of positive equilibrium position 2 EP by finding the variational matrix 2…”

Section: Dynamics Of Stability In Positive Equilibrium Position Ofmentioning

confidence: 99%

“…A characteristic behavior of chaos is the dependence on the sensitivity to initial points. To exhibit the sensitivity to initial values of model (2), two paths 00 ( 0.0001, ) xy  and 00 ( , 0.0001) xy are considered with initial points 00 ( , ) xy respectively. The results are established and presented in Figure…”

Section: A Sensitive Analysismentioning

confidence: 99%

“…Dynamics of Stability at Interior Equilibrium Position of the System (2)VI. ANALYSIS OF PERIODIC-DOUBLING BIFURCATIONSIn this section, bifurcation theory is applied in order to examine the existence of period-doubling (flip) bifurcation at axial equilibrium position 1 EP for the system (6) and positive equilibrium position 2 EP of the model(2). Let …”

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confidence: 99%

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Stability and Bifurcation: Discrete Differential Algebraic Planar Model with Square Root Response

2020

IJRTE

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Abstract: The stability and existence of bifurcation analysis for a two spices discrete time model by introducing square root functional response and step size is examined in this work. Forward Euler scheme method is applied to formulate the discrete model from the continuous model, particularly to explore the rich dynamical behavior of the proposed model. Because the model has square root response function, trivial and axial equilibrium positions are singular. In order to discuss the stability of the trivial and axial equilibrium positions, a transformation is applied. Moreover, we explore the stability of the interior equilibrium position in a discrete two spices model using jury conditions. The numerical experiments are performed for distinct parameter values and also time series and phase line diagrams are presented. We also apply bifurcation theory to find whether the model of spices undergoes periodic doubling bifurcation at its axial and interior equilibrium positions. Numerical examples are provided and they exhibit rich dynamics in both species, including, period -2, 4, 8 & 16 orbits, periodic windows and Non periodic orbit(chaos).

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“…In ecology, several authors discussed the dynamics of predator-prey model and contributed to the development of the population dynamics [2,6,13].…”

Section: Stability and Bifurcation: Discrete Differentialmentioning

confidence: 99%

Section: Equilibrium Positions and Variational Matrix Of Model (2)mentioning

confidence: 99%

“…We investigate the stability of positive equilibrium position 2 EP by finding the variational matrix 2…”

Section: Dynamics Of Stability In Positive Equilibrium Position Ofmentioning

confidence: 99%

Section: A Sensitive Analysismentioning

confidence: 99%

mentioning

confidence: 99%

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Stability and Bifurcation: Discrete Differential Algebraic Planar Model with Square Root Response

2020

IJRTE

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Dynamical complexities in a predator-prey system involving teams of two prey and one predator

Mishra

Raw

2019

J. Appl. Math. Comput.

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A comparison of ecological and eco-evolutionary system with rapid predator evolution

Samanta¹,

Sahoo²,

Das³

2020

Int. J. Dynam. Control

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Complex dynamics in a ratio-dependent two-predator one-prey model

Cited by 12 publications

References 32 publications

Stability and Bifurcation: Discrete Differential Algebraic Planar Model with Square Root Response

Stability and Bifurcation: Discrete Differential Algebraic Planar Model with Square Root Response

Dynamical complexities in a predator-prey system involving teams of two prey and one predator

A comparison of ecological and eco-evolutionary system with rapid predator evolution

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