Effort dynamics of a delay-induced prey–predator system with reserve

Chakraborty, Kunal; Jana, Soovoojeet; Kar, Tapan Kumar

doi:10.1007/s11071-012-0575-z

Cited by 37 publications

(50 citation statements)

References 36 publications

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“…When ℎ = 0.2, = 0.2, = 5.7, and initial states are (10,15,11), the dynamic behavior is chaotic. Assume that 1 ∈ [− 4 , 4 ] and 4 > 0; then Chen system can be exactly represented by T-S fuzzy model as follows: …”

Section: Fuzzy Modeling Of Rossler's System As Functional Systemmentioning

confidence: 99%

“…It means these states are always in the first quadrant, such as the three species prey-predator systems [15,16,21], double Mackey-Glass systems [17,22,23], energy communication system in biological research [19,24], and virus-immune system [20]. For the three species preypredator systems, which consist of two competing preys and one predator can be described by the following set of nonlinear differential equations: = 1, 2 represent the densities of the two prey species and represents the density of the predator species.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy

Chen

Lin

et al. 2015

Abstract and Applied Analysis

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A novel bioinspired control strategy design is proposed for generalized synchronization of nonlinear chaotic systems, combining the bioinspired stability theory, fuzzy modeling, and a novel, simple-form Lyapunov control function design of derived high efficient, heuristic and bioinspired controllers. Three main contributions are concluded: (1) apply the bioinspired stability theory to further analyze the stability of fuzzy error systems; the high performance of controllers has been shown in previous study by Li and Ge 2009, (2) a new Lyapunov control function based on bioinspired stability theory is designed to achieve synchronization without using traditional LMI method, which is a simple linear homogeneous function of states and the process of designing controller to synchronize two fuzzy chaotic systems becomes much simpler, and (3) three different situations of synchronization are proposed; classical master and slave Lorenz systems, slave Chen's system, and Rossler's system as functional system are illustrated to further show the effectiveness and feasibility of our novel strategy. The simulation results show that our novel control strategy can be applied to different and complicated control situations with high effectiveness.

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Section: Fuzzy Modeling Of Rossler's System As Functional Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy

Chen

Lin

et al. 2015

Abstract and Applied Analysis

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“…effectively used different mathematical models to describe the interactions between prey and the predator species. Some more theoretical works on different types of dynamical behaviors of prey-predator system can be observed in Yan and Liu [8], Zhang et al [9], Jana and Kar [10,11], Kar and Jana [12], Chakraborty et al [13] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Global dynamics of a predator, weaker prey and stronger prey system

Jana¹,

Ghorai²,

Guria³

et al. 2015

Applied Mathematics and Computation

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“…Sana and Chaudhuri [4] and Sana [5] developed a harvesting model of fisheries and poultry of birds in crisp environment. The stability of biomathematical models are developed in crisp environment by Bunomo et al [6], Chakraborty et al [7,8], Zhou [9], Jiang et al [10] and others. But in reality they are not precise in nature.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of combined project of fish, broiler and ducks: Dynamical system in imprecise environment

Maity²,

Maiti

2015

Int. J. Biomath.

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In this paper, we consider three species harvesting model and develop a solution procedure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval numbers. A parametric mathematical program is formulated to find the biological equilibrium of the model for different values of parameters. This interval-valued problem is converted into equivalent crisp model using interval operations. The main advantage of the proposed procedure is that we can present different characteristics of the model in a single framework. Analytically, the existence of steady state and stabilities are looked into. Using mathematical software, the model is illustrated and the results are obtained and presented in tabular and graphical forms. Int. J. Biomath. 2015.08. Downloaded from www.worldscientific.com by MCMASTER UNIVERSITY on 09/30/15. For personal use only. A. De, K. Maity & M. Maiti 1550067-2 Int. J. Biomath. 2015.08. Downloaded from www.worldscientific.com by MCMASTER UNIVERSITY on 09/30/15. For personal use only.Stability analysis of combined project of fish, broiler and ducks or a suitable probability distribution for the imprecise biological parameters. In the development of the above models, there are some lacunas in the formulation and solution of the models. These are:• None formulated a joint project of three related biological species such as fish, broiler and duck and studied the system. • None evaluated the three species system with uncertain biological parameters such as interval or fuzzy parameters.In this paper, we consider three species dynamic model and develop a solution procedure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval numbers. A parametric mathematical program is formulated to find the behavior of the model (biological equilibrium) for different values of parameters. The proposed procedure is more effective and interesting since we get different behavior of the model using functional form of an interval parameter for different values of parameters. We develop a new procedure to study this three species dynamic model using interval-valued technique. The main advantage of the proposed procedure is that we can present different characteristics of the model in a single framework.The paper is organized as follows. In Sec. 2, we discuss some prerequisite mathematics on interval numbers and Sec. 3 for notations. In Sec. 4, we formulate the model with crisp data. In Sec. 5, the model is extended in imprecise environment. We discuss the boundedness of the system in Sec. 6 and the local stability of the imprecise model in Sec. 7. Some particular cases have been discussed in Sec. 8. We have discussed a brief description of the results and figures of the numerical experiment in Sec. 9. This paper is concluded in Sec. 10. Prerequisite Mathematics An interval number A is represented by closed interval [a l , a u ] and defined bywhere R is the set of all real numbers and a l , a u are t...

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Effort dynamics of a delay-induced prey–predator system with reserve

Cited by 37 publications

References 36 publications

Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy

Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy

Global dynamics of a predator, weaker prey and stronger prey system

Stability analysis of combined project of fish, broiler and ducks: Dynamical system in imprecise environment

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