Dynamic Properties of the Predator–Prey Discontinuous Dynamical System

Elsayed, Ahmed; Nasr, Mohamed E.

doi:10.5560/zna.2011-0051

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Discontinuous Dynamical Systems1

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Cited by 4 publications

(3 citation statements)

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“…which implies that the solution of the problem (1)- (2) is discontinuous (sectionally continuous) on (0, T ] and thus we have proved the following theorem [7]. …”

Section: Introductionmentioning

confidence: 82%

On Some Dynamics of Duffing Dynamical System Generated by a Semi-Discretization Process with Two Different Delays

El‐Sayed¹,

El-Raheem²,

Salman³

2014

Math. Sci. Lett.

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“…which implies that the solution of the problem (1)- (2) is discontinuous (sectionally continuous) on (0, T ] and thus we have proved the following theorem [7]. …”

Section: Introductionmentioning

confidence: 82%

On Some Dynamics of Duffing Dynamical System Generated by a Semi-Discretization Process with Two Different Delays

El‐Sayed¹,

El-Raheem²,

Salman³

2014

Math. Sci. Lett.

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“…The discontinuous dynamical systems have been studied, recently, in [3]- [5]. The results in [4] and [5] shows the richness of the models of discontinuous dynamical systems. Consider the problem of retarded functional equation…”

Section: Discontinuous Dynamical Systemsmentioning

confidence: 99%

Discontinuous dynamical system represents the Logistic retarded functional equation with two different delays

El-Sayed

Nasr

2013

Malaya J. Mat.

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In this work we are concerned with the discontinuous dynamical system representing the problem of the logistic retarded functional equation with two different delays,$$\begin{aligned}& x(t)=\rho x\left(t-r_1\right)\left[1-x\left(t-r_2\right)\right], \quad t \in(0, T], \\& x(t)=x_0, \quad t \leq 0 .\end{aligned}$$The existence of a unique solution $x \in L^1[0, T]$ which is continuously dependence on the initial data, will be proved. The local stability at the equilibrium points will be studied. The bifurcation analysis and chaos will be discussed.

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“…and (2) show the trajectories of (2.1) and (2.2) when r = 1 respectively, while Figures(3) and (4) show the trajectories of (2.3) and (2.4), respectively.…”

mentioning

confidence: 99%

Chaos and bifurcation of the Logistic discontinuous dynamical systems with piecewise constant arguments

Elsayed¹,

Salman²

2013

Malaya J. Mat.

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In this paper we are concerned with the definition and some properties of the discontinuous dynamical systems generated by piecewise constant arguments. Then we study two discontinuous dynamical system of the Logistic equation as an example. The local stability at the fixed points is studied. The bifurcation analysis and chaos are discussed. In addition, we compare our results with the discrete dynamical systems of the Logistic equation.

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Dynamic Properties of the Predator–Prey Discontinuous Dynamical System

Abstract: In this work, we study the dynamic properties (equilibrium points, local and global stability, chaos and bifurcation) of the predator-prey discontinuous dynamical system. The existence and uniqueness of uniformly Lyapunov stable solution will be proved.

Cited by 4 publications

References 2 publications

On Some Dynamics of Duffing Dynamical System Generated by a Semi-Discretization Process with Two Different Delays

On Some Dynamics of Duffing Dynamical System Generated by a Semi-Discretization Process with Two Different Delays

Discontinuous dynamical system represents the Logistic retarded functional equation with two different delays

Chaos and bifurcation of the Logistic discontinuous dynamical systems with piecewise constant arguments

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