Pattern formation and control of spatiotemporal chaos in a reaction diffusion prey–predator system supplying additional food

Ghorai, Santu; Poria, Swarup

doi:10.1016/j.chaos.2016.01.013

Cited by 34 publications

(8 citation statements)

References 25 publications

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“…. Following Elsadany and Matouk [11], and El-Sayed and Salman [18], the discretization process of model (3) can be performed to obtain (4) Notice that if then model (4) becomes the Euler discretization of model (1).…”

Section: Wherementioning

confidence: 99%

“…In ecology, understanding the dynamical relationship between prey and predator are center of goal [1]. Relationship between prey and predator plays important role for universal existence [2].…”

Section: Introduction mentioning

confidence: 99%

“…Recently, Ghosh et al introduced the following prey-predator model with prey refuge and additional food for predator [5]. (1) where and denote the density of prey and predator with all parameters are positive. Model (1) explain that prey population grows logistically with environmental carrying capacity .…”

Section: Introduction mentioning

confidence: 99%

“…(1) where and denote the density of prey and predator with all parameters are positive. Model (1) explain that prey population grows logistically with environmental carrying capacity . In the second part of right-hand-side the prey population, parameter characterize as predation rate on prey by modified functional respon Holling-type II.…”

Section: Introduction mentioning

confidence: 99%

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Numerical Solution of a Fractional-Order Predator-Prey Model with Prey Refuge and Additional Food for Predator

Satriyantara

Suryanto

Hidayat

2018

JELS

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In this paper, a fractional-order predator-prey model with prey refuge and additional food for predator is solved numerically. For that aim, the model is discretized using a piecewise constant arguments. The equilibrium points of the discrete fractional-order model are investigated. Numerical simulations are conducted to see the stability of each equilibrium point. The numerical simulations show that stability of the equilibrium points is dependent on the time step.

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Section: Wherementioning

confidence: 99%

Section: Introduction mentioning

confidence: 99%

Section: Introduction mentioning

confidence: 99%

Section: Introduction mentioning

confidence: 99%

See 2 more Smart Citations

Numerical Solution of a Fractional-Order Predator-Prey Model with Prey Refuge and Additional Food for Predator

Satriyantara

Suryanto

Hidayat

2018

JELS

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“…Since Alan Turing put forward the reaction diffusion equations of chemical and found that diffusion could destabilize the stable equilibrium [6]. Currently, reaction-diffusion theory is gradually maturing and is applied into many fields [5,7].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of a Ratio-Dependent Holling-Tanner Model with Cross-Diffusion

Li¹,

Yan²,

Ye³

2018

Proceedings of the 2018 3rd International Conference on Communications, Information Management and Network Security (CIMNS 2018

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In this paper, we investigate a discrete space-time predator-prey model with ratio-dependent function response. The model is given by a coupled map lattice framework, it takes a nonlinear relationship between predator-prey reaction stage and dispersal stage. Through stability analysis and bifurcation analysis, the parameter conditions of Hopf bifurcation is obtained. When adding the cross-diffusion, we obtain the parameter conditions of Turing instability. Numerical simulations verify the theoretical analysis and show a series of spatial patterns.

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Stability and bifurcation analysis of delayed tri‐trophic food chain model in poisoned environment with fear effect and additional food

Sivasamy

Banjerdpongchai

Park

2023

Math Methods in App Sciences

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One of the most important goals of theoretical ecologists is to find a strategy for controlling the chaos in ecological models to maintain healthy ecosystems. We investigate the influence of fear and the supply of additional food to predators in a delayed tri‐trophic food chain model, where interference among the species is determined by Holling type‐II functional response. The proposed model incorporates the fact that the growth rates of prey and middle predators are decreased due to the fear of middle and special predators, respectively. The additional food is supplied to both predators by either nature or external agencies. Furthermore, the poisoned prey in the predator's environment is taken into account. In the proposed model, we use two time delays: one for the growth term of the middle predator and another for the gestation delay of the special predator. We determine the conditions for the existence of ecologically feasible equilibrium points and their local and global stability. In addition, we establish the conditions for the existence of Hopf bifurcation around interior equilibrium to seek periodic behavior in nondelayed and delayed models. Numerical investigations are performed to justify the proposed theoretical findings through phase portraits, time series of solutions, and bifurcation diagrams. We observe that the chaotic dynamics of a tri‐trophic food chain model can be controlled by the proper choice of the fear effect and by supplying additional food parameters. As a result, our findings provide more ecological insights into the dynamics of the delayed tri‐trophic food chain model with the fear effect and additional food supply.

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Pattern formation and control of spatiotemporal chaos in a reaction diffusion prey–predator system supplying additional food

Cited by 34 publications

References 25 publications

Numerical Solution of a Fractional-Order Predator-Prey Model with Prey Refuge and Additional Food for Predator

Numerical Solution of a Fractional-Order Predator-Prey Model with Prey Refuge and Additional Food for Predator

Bifurcation Analysis of a Ratio-Dependent Holling-Tanner Model with Cross-Diffusion

Stability and bifurcation analysis of delayed tri‐trophic food chain model in poisoned environment with fear effect and additional food

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