Species extinction and permanence of an impulsively controlled two-prey one-predator system with seasonal effects

Baek, Hunki

doi:10.1016/j.biosystems.2009.06.008

Cited by 24 publications

(27 citation statements)

References 36 publications

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“…The system permanence in a impulsively controlled two-prey one-predator system was discussed in (cf. [14][15][16]). Bio-economic model considering linear and hyperbolic response functions for preys and finding out the optimal harvesting policy in interior equilibrium was studied in (cf.…”

Section: Introductionmentioning

confidence: 97%

Stability analysis of a food chain model consisting of two competitive preys and one predator

Ali¹,

Chakravarty

2015

Nonlinear Dyn

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The present article deals with the intraspecific competition among predator populations of a prey-dependent three-component food chain model system consisting of two competitive preys and one predator. The behaviour of the system near the biologically feasible equilibria is thoroughly analysed. Boundedness and dissipativeness of the system are established. The stability analysis including local and global stability of the equilibria has been carried out in order to examine the behaviour of the system. The present system experiences Hopf-Andronov bifurcation for suitable choice of parameters. The results of this investigation reveal that the intra-specific competition among predator populations can be beneficial for the survival of predator. The ecological implications of both the analytical and the numerical findings are discussed at length towards the end.

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Section: Introductionmentioning

confidence: 97%

Stability analysis of a food chain model consisting of two competitive preys and one predator

Ali¹,

Chakravarty

2015

Nonlinear Dyn

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“…Recently, a few studies on permanence of general nonautonomous impulsive systems (1) and (2) and their special cases were made in [1,5,20,21,2,6,7,23,24,12,[25][26][27][28]30,31,35,17,36,18,4]. Therefore, applying Theorem 1 and Corollary 1 of this paper we obviously can obtain that if systems are ω-periodic, then there is at least one positive ω-periodic solution under the permanent conditions.…”

Section: Remarkmentioning

confidence: 76%

“…For more details see Theorem 3.1 in [19]. At the same time, we also see that the dynamical properties for many special cases of systems (1) and (2) have been extensively studied, for example [1,5,20,21,2,3,22,6,7,[23][24][25][26][27][28][29][30][31][32][33]8,[34][35][36] and the references cited therein. The main study subjects are the permanence, persistence and extinction of species, the local and global asymptotic stability of systems, the existence and uniqueness of positive periodic solution and almost periodic solution, and the bifurcation and dynamical complexity, etc.…”

Section: Introductionmentioning

confidence: 97%

The periodic solutions for general periodic impulsive population systems of functional differential equations and its applications

Teng

Nie

Fang

2011

Computers & Mathematics with Applications

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a b s t r a c tIn this paper, the general periodic impulsive population systems of functional differential equations are investigated. By using the method of Poincare map and Horn's fixed point theorem, we prove that the ultimate boundedness of all solutions implies the existence of periodic solutions. As applications of this result, the existence of positive periodic solutions for the general periodic impulsive Kolmogorov-type population dynamical systems are discussed. We further prove that as long as the system is permanent, there must exist at least one positive periodic solution. In addition, the permanence and existence of positive periodic solutions are discussed for the periodic impulsive single-species logistic models and the periodic impulsive n-species Lotka-Volterra competitive models with delays.

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“…It may change the dynamics of ecological systems; the importance of seasonal variation is in its actual presence in nature [5] . Seasonality on ecological systems has been studied theoretically by some researchers [5], [6], [7], [8], [9]. The sinusoid function is the most popular method that has been used to describe temporal variation in ecological models [6], [10], [11].…”

Section: Introductionmentioning

confidence: 99%

Simulation of complex dynamical behavior in prey predator model

Alebraheem

Abu-Hassan

2012

2012 International Conference on Statistics in Science, Business and Engineering (ICSSBE)

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Species extinction and permanence of an impulsively controlled two-prey one-predator system with seasonal effects

Cited by 24 publications

References 36 publications

Stability analysis of a food chain model consisting of two competitive preys and one predator

Stability analysis of a food chain model consisting of two competitive preys and one predator

The periodic solutions for general periodic impulsive population systems of functional differential equations and its applications

Simulation of complex dynamical behavior in prey predator model

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