Chaos in three species ratio dependent food chain

Gakkhar, Sunita; Naji, Raid Kamel

doi:10.1016/s0960-0779(02)00038-3

Cited by 48 publications

(23 citation statements)

References 5 publications

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“…Through numerical simulations they had shown the existence of chaos in the model for biologically feasible parametric values. The presence of chaotic nature in three species food chain/web models has also been established in [12,15].…”

Section: Introductionmentioning

confidence: 96%

Complex behaviour in four species food-web model

Gakkhar¹,

Priyadarshi²,

Banerjee³

2012

Journal of Biological Dynamics

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A four-dimensional food-web system consisting of a bottom prey, two middle predators and a generalist predator has been developed with modified functional response. The system is well posed and dissipative. Some results on uniform persistence have been developed. The dynamics of the system is found to be chaotic for certain choice of parameters. The coexistence of all four species is possible in the form of periodic orbits/strange attractors for suitably chosen set of parameters.

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Section: Introductionmentioning

confidence: 96%

Complex behaviour in four species food-web model

Gakkhar¹,

Priyadarshi²,

Banerjee³

2012

Journal of Biological Dynamics

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“…Several ecological circumstances have been analyzed by interaction between two or more species. The system representing the interaction between three species shows complex dynamical behavior [3,4,6,7,8,12]. The interaction of species involving persistence and extinction have been the area of interest for researchers [1,5,11,13].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Behaviour in Two Prey-Predator System with Persistence

Madhusudanan¹,

Vijaya

2016

BMSA

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Abstract. In this work, the dynamical behavior of the system with two preys and one predator population is investigated. The predator exhibits a Holling type II response to one prey which is harvested and a Beddington-DeAngelis functional response to the other prey. The boundedness of the system is analyzed. We examine the occurrence of positive equilibrium points and stability of the system at those points. At trivial equilibrium E 0 and axial equilibrium (E 1 ), the system is found to be unstable. Also we obtain the necessary and sufficient conditions for existence of interior equilibrium point (E 6 ) and local and global stability of the system at the interior equilibrium (E 6 ). Depending upon the existence of limit cycle, the persistence condition is established for the system. The numerical simulation infer that varying the parameters such as e and λ 1 it is possible to change the dynamical behavior of the system from limit cycle to stable spiral. It is also observed that the harvesting rate plays a crucial role in stabilizing the system.

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“…Ayala [10] proved experimentally that two species of Drosophila could coexist upon a single limit resource. Ayala's experiment leads to a large body of work, which continuous to this day, see [1,2,6,8,[15][16][17][19][20][21][22][23][24][25]. Upadhyay [20] studied Rosenzweig-McArthur [18] model to investigate the existence of complex dynamical behavior in a food chain model involving Holling type IV functional response of the form wx d+x+x 2 /i and the effects of the intraspecific competition in the first level of the model is also studied.…”

Section: Introductionmentioning

confidence: 99%

Controlling Chaotic Dynamics of a Continuous Ecological Model

al.¹

2016

Int. J. of Pure and Appl. Math.

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In this paper a technique of controlling chaotic behavior of a three species food chain model with Sokol-Howell functional response by involving intraspecific competition is discussed. The model is proved to be dissipative in the positive octant. Controlling conditions of chaotic behavior of the system are carried out. Stability analysis of the equilibrium points is analyzed. Lyaponuv exponents and bifurcation diagrams are used to study the complex dynamics of the model. The impact of the intraspecific competition in the dynamics of the food chain model with Sokol-Howell response is investigated theoretically as well as numerically.

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Chaos in three species ratio dependent food chain

Cited by 48 publications

References 5 publications

Complex behaviour in four species food-web model

Complex behaviour in four species food-web model

Dynamical Behaviour in Two Prey-Predator System with Persistence

Controlling Chaotic Dynamics of a Continuous Ecological Model

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