Bifurcation and chaos in discrete-time predator–prey system

Jing, Zhujun; Yang, Jianping

doi:10.1016/j.chaos.2005.03.040

Cited by 169 publications

(104 citation statements)

References 20 publications

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“…In this paper, we design a proper controller to control the chaos of system (1) which was firstly studied by Zhang and Li [6]. From the theoretical analysis, we concluded that the control variable where P T is given by Equation (4).…”

Section: Resultsmentioning

confidence: 99%

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Chaos Control in a Discrete Ecological System

Zhang¹,

Zhang²

2012

IJMNTA

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In research [1], the authors investigate the dynamic behaviors of a discrete ecological system. The period-double bifurcations and chaos are found in the system. But no strategy is proposed to control the chaos. It is well known that chaos control is the first step of utilizing chaos. In this paper, a controller is designed to stabilize the chaotic orbits and enable them to be an ideal target one. After that, numerical simulations are presented to show the correctness of theoretical analysis.

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Section: Resultsmentioning

confidence: 99%

“…In recent years, the study of discrete ecological systems has attracted extensive attentions [1][2][3][4][5][6]. This is because that some natural populations have non-overlapping generations, thus discrete models are more realistic than continuous ones to study these species.…”

Section: Introductionmentioning

confidence: 99%

Chaos Control in a Discrete Ecological System

Zhang¹,

Zhang²

2012

IJMNTA

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“…[32][33][34] and good results were obtained about its higher precisions brought in the study of the various systems described by it. The graph of Figure.1 shows the potential energy.…”

Section: Model and Equationsmentioning

confidence: 99%

Signature of chaos in the semi quantum behavior of a classically regular triple well heterostructure

Lekeufack¹,

Yamgoué²,

Kofané³

2010

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We analyze the phenomenon of semiquantum chaos in the classically regular triple well model from classical to quantum. His dynamics is very rich because it provides areas of regular behavior, chaotic ones and multiple quantum tunneling depending on the energy of the system as the Planck's constant  varies from 0 to 1.The Time Dependent Variational Principle TDVP using generalized Gaussian trial wave function, which, in many-body theory leads to the Hartree Fock Approximation TDHF, is added to the techniques of Gaussian effective potentials and both are used to study the system. The extended classical system with fluctuation variables nonlinearly coupled to the average variables exhibit energy dependent transitions between regular behavior and semi quantum chaos monitored by bifurcation diagram together with some numerical indicators.

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“…Both the logistic equation and the predator-prey interaction model coming from ecology and can be applied to urban studies [24]. The predator-prey system can be modeled by different mathematical expressions, which can produce period-doubling bifurcation and chaos [9,[30][31][32]. On the one hand, the bifurcation and chaos proceeding from the twodimension mapping of urbanization dynamics remind us of the complicated behaviors shown by the one-dimension logistic mapping of insect population.…”

Section: Generalization and Suppositionmentioning

confidence: 99%

Reinterpreting the Origin of Bifurcation and Chaos by Urbanization Dynamics

Chen¹

2018

Chaos Theory

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Chaos associated with bifurcation makes a new science, but the origin and essence of chaos are not yet clear. Based on the well-known logistic map, chaos used to be regarded as intrinsic randomicity of determinate dynamics systems. However, urbanization dynamics indicates new explanation about it. Using mathematical derivation, numerical computation, and empirical analysis, we can explore chaotic dynamics of urbanization. The key is the formula of urbanization level. The urbanization curve can be described with the logistic function, which can be transformed into one-dimensional map and thus produce bifurcation and chaos. On the other hand, the logistic model of urbanization curve can be derived from the rural-urban population interaction model, which can be discretized to a two-dimensional map. An interesting finding is that the two-dimensional rural-urban coupling map can create the same bifurcation and chaos patterns as those from the one-dimensional logistic map. This suggests that the urban bifurcation and chaos come from spatial interaction between rural and urban populations rather than pure intrinsic randomicity of determinate models. This discovery provides a new way of looking at origin and essence of bifurcation and chaos in physical and social sciences.

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Bifurcation and chaos in discrete-time predator–prey system

Cited by 169 publications

References 20 publications

Chaos Control in a Discrete Ecological System

Chaos Control in a Discrete Ecological System

Signature of chaos in the semi quantum behavior of a classically regular triple well heterostructure

Reinterpreting the Origin of Bifurcation and Chaos by Urbanization Dynamics

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