Bifurcation analysis and chaos control in discrete-time glycolysis models

Din, Qamar

doi:10.1007/s10910-017-0839-4

Cited by 64 publications

(28 citation statements)

References 28 publications

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“…On the other hand, population models with non-overlapping generations have more irregular complex behaviour. For some recent investigation related to chaos control in discrete-time models we refer to [1,[13][14][15][16][17][18][19][20][22][23][24] and references are therein. In this section, first we discuss pole-placement chaos control method based on state feedback control which was introduced by Romeiras et al [44] (also see [41]).…”

Section: Chaos Controlmentioning

confidence: 99%

Bifurcation analysis and chaos control for a plant–herbivore model with weak predator functional response

Din¹,

Shabbir

Ahmad

2019

Journal of Biological Dynamics

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The interaction between plants and herbivores is one of the most fundamental processes in ecology. Discrete-time models are frequently used for describing the dynamics of plants and herbivores interaction with non-overlapping generations, such that a new generation replaces the old at regular time intervals. Keeping in view the interaction of the apple twig borer and the grape vine, the qualitative behaviour of a discrete-time plant-herbivore model is investigated with weak predator functional response. The topological classification of equilibria is investigated. It is proved that the boundary equilibrium undergoes transcritical bifurcation, whereas unique positive steady-state of discrete-time plant-herbivore model undergoes Neimark-Sacker bifurcation. Numerical simulation is provided to strengthen our theoretical discussion. ARTICLE HISTORY

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Section: Chaos Controlmentioning

confidence: 99%

Bifurcation analysis and chaos control for a plant–herbivore model with weak predator functional response

Din¹,

Shabbir

Ahmad

2019

Journal of Biological Dynamics

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“…Furthermore, the implementation for such a hybrid control strategy is comparatively simple one and it is based on both parameter perturbation and state feedback control strategy. It is worthwhile to mention some other investigations for controlling chaos in discrete-time systems and the interested reader is referred to [22][23][24][25][26][27][28][29][30][31].…”

Section: Chaos Controlmentioning

confidence: 99%

Bifurcation and chaos control in a discrete-time predator–prey model with nonlinear saturated incidence rate and parasite interaction

et al. 2019

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The dynamical behavior of the predator-prey system is influenced effectively due to the mutual interaction of parasites. Regulations are imposed on biodiversity due to such type of interaction. With implementation of nonlinear saturated incidence rate and piecewise constant argument method of differential equations, a three-dimensional discrete-time model of prey-predator-parasite type is studied. The existence of equilibria and the local asymptotic stability of these steady states are investigated. Moreover, explicit criteria for a Neimark-Sacker bifurcation and a period-doubling bifurcation are implemented at positive equilibrium point of the discrete-time model. Chaos control is discussed through implementation of a hybrid control technique based on both parameter perturbation and a state feedback strategy. At the end, some numerical simulations are provided to illustrate our theoretical discussion.

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“…Recently, many iterated maps have been studied for existence and direction of Neimark-Sacker bifurcation (cf. [37][38][39][40][41][42][43][44][45][46][47][48][49][50]).…”

Section: Neimark-sacker Bifurcationmentioning

confidence: 99%

A dynamically consistent nonstandard finite difference scheme for a predator–prey model

et al. 2019

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The interaction between prey and predator is one of the most fundamental processes in ecology. Discrete-time models are frequently used for describing the dynamics of predator and prey interaction with non-overlapping generations, such that a new generation replaces the old at regular time intervals. Keeping in view the dynamical consistency for continuous models, a nonstandard finite difference scheme is proposed for a class of predator-prey systems with Holling type-III functional response. Positivity, boundedness, and persistence of solutions are investigated. Analysis of existence of equilibria and their stability is carried out. It is proved that a continuous system undergoes a Hopf bifurcation at its interior equilibrium, whereas the discrete-time version undergoes a Neimark-Sacker bifurcation at its interior fixed point. A numerical simulation is provided to strengthen our theoretical discussion.

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Bifurcation analysis and chaos control in discrete-time glycolysis models

Cited by 64 publications

References 28 publications

Bifurcation analysis and chaos control for a plant–herbivore model with weak predator functional response

Bifurcation analysis and chaos control for a plant–herbivore model with weak predator functional response

Bifurcation and chaos control in a discrete-time predator–prey model with nonlinear saturated incidence rate and parasite interaction

A dynamically consistent nonstandard finite difference scheme for a predator–prey model

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