Bifurcation and chaotic behavior of a discrete singular biological economic system

Chen, Boshan; Chen, Jie‐Jie

doi:10.1016/j.amc.2012.07.043

Cited by 39 publications

(30 citation statements)

References 32 publications

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“…C haotic systems are very complex nonlinear systems where their responses display some particular features such as excessive sensitivity to the initial situations, comprehensive Fourier transform spectrums, and irregular behaviors of the motion in phase space [1][2][3][4]. The chaos concept is very beneficial in analyzing fundamental problems such as collapse prevention of power systems [5], chemical processing [6], information processing [7], secure communication [8], centrifugal flywheel governor [9], biolog-ical engineering [10], rotating mechanical systems [11], highperformance circuits and devices [12], and so forth. In the past few years, the stabilization and tracking control of chaotic systems have been paid much attention [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Finite‐time stabilization of a class of chaotic systems with matched and unmatched uncertainties: An LMI approach

Mobayen

2014

Complexity

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This article investigates the sliding mode control method for a class of chaotic systems with matched and unmatched uncertain parameters. The proposed reaching law is established to guarantee the existence of the sliding mode around the sliding surface in a finite-time. Based on the Lyapunov stability theory, the conditions on the state error bound are expressed in the form of linear matrix inequalities. Simulation results for the well-known Genesio's chaotic system are provided to illustrate the effectiveness of the proposed scheme.

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Section: Introductionmentioning

confidence: 99%

Finite‐time stabilization of a class of chaotic systems with matched and unmatched uncertainties: An LMI approach

Mobayen

2014

Complexity

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“…There are many investigations for predator-prey models [2][3][4][5][6][7][8][9][10][11][12] and [23,25]. In recent years, the discrete-time population models have attracted more and more attention.…”

Section: Introductionmentioning

confidence: 99%

“…The discrete-time models sometimes have richer dynamical behaviors. For instance, the single-species discrete-time models have bifurcations, chaos and more complex dynamical behaviors (see [6,[12][13][14][15][16][18][19][20][21][22]). For the flip bifurcation and Hopf bifurcation of discrete models, see also [6,[12][13][14]24].…”

Section: Introductionmentioning

confidence: 99%

Complex dynamics of a discrete predator–prey system with a strong Allee effect on the prey and a ratio-dependent functional response

Fang

2018

Adv Differ Equ

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In this paper, we consider the complex dynamics of a discrete predator-prey system with a strong Allee effect on the prey and a ratio-dependent functional response, which is the discrete version of the continuous system in (Nonlinear Anal., Real World Appl. 16:235-249, 2014). First, by giving several examples to display the limitations and errors of the local stability of the equilibrium point p obtained in (Nonlinear Anal., Real World Appl. 16:235-249, 2014), we provide an easily verified and complete discrimination criterion for the local stability of this equilibrium. Then we study some properties of its discrete version, especially for the stability and bifurcation for the equilibrium point E 1 , which has not been considered in any literature to the best of our knowledge. By using the center manifold theorem and bifurcation theory, we consider the flip bifurcation of this system at E 1 and obtain the stability of the closed orbits bifurcated from E 1 . The numerical simulations not only show the correctness of our theoretical analysis, but also we find some new and interesting dynamics of this system.

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“…Ghaziani et al [9] studied the resonance and bifurcation in a discrete-time predator-prey system with Holling functional response. Chen et al [7] applied the forward Euler method to the ratio-dependent predator-prey model, and then investigated the dynamical behaviors of its discrete system by using the center manifold theorem. Elabbasy et al [8] derived the existence and stability of the fixed points of a discrete reduced Lorenz system by using the center manifold theorem and bifurcation theory.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis in a discrete SIR epidemic model with the saturated contact rate and vertical transmission

Du¹,

Zhang²,

Qin³

et al. 2016

J. Nonlinear Sci. Appl.

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The aim of paper is dealing with the dynamical behaviors of a discrete SIR epidemic model with the saturated contact rate and vertical transmission. More precisely, we investigate the local stability of equilibriums, the existence, stability and direction of flip bifurcation and Neimark-Sacker bifurcation of the model by using the center manifold theory and normal form method. Finally, the numerical simulations are provided for justifying the validity of the theoretical analysis.

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Bifurcation and chaotic behavior of a discrete singular biological economic system

Cited by 39 publications

References 32 publications

Finite‐time stabilization of a class of chaotic systems with matched and unmatched uncertainties: An LMI approach

Finite‐time stabilization of a class of chaotic systems with matched and unmatched uncertainties: An LMI approach

Complex dynamics of a discrete predator–prey system with a strong Allee effect on the prey and a ratio-dependent functional response

Bifurcation analysis in a discrete SIR epidemic model with the saturated contact rate and vertical transmission

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