Periodic solutions for predator–prey systems with Beddington–DeAngelis functional response on time scales

Fazly, Mostafa; Hesaaraki, Mahmoud

doi:10.1016/j.nonrwa.2007.02.012

Cited by 35 publications

(22 citation statements)

References 8 publications

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“…Note that J = I ( the identical mapping), since ImQ = KerL, according to the invariance property of homotopy, direct calculation produces Remark 3.1. If we only consider the prey population in one-patch environment and ignore the dispersal process in the system (1.4), and if τ 11 ≡ τ 21 ≡ 0 in (1.4), then the system (1.4) reduces to the standard two species predator-prey model with Beddington-DeAngelis functional response on time scales investigated in [3] and [9]. Theorem 3.1 generalizes the main results of them.…”

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confidence: 59%

Existence of periodic solutions to a system with functional response on time scales

Liu

2009

Anal. Theory Appl.

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This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the system. Moreover, when the time scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the method is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference equations.

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confidence: 59%

Existence of periodic solutions to a system with functional response on time scales

Liu

2009

Anal. Theory Appl.

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“…For example, it can model insect populations that are continuous while in season (and may follow a di erence scheme with variable step-size), die out in winter, while their eggs are incubating or dormant, and then hatch in a new season, giving rise to a nonoverlapping population. The study of population dynamic systems on time scales can reveal new qualitative phenomenon, see, for example, [2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Nabla inequalities and permanence for a logistic integrodifferential equation on time scales

Wang

2017

Open Mathematics

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In this paper, by using the theory of calculus on time scales and some mathematical methods, several nabla dynamic inequalities on time scales are established. As an application, we apply the obtained results to a logistic integrodi erential equation on time scales and su cient conditions for the permanence of the equation are derived. Finally, numerical examples together with their simulations are presented to illustrate the feasibility and e ectiveness of the results.

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“…To unify the study of differential and difference equations, the theory of Time Scales Calculus is initiated by Stephan Hilger. In [20] [21], unification of the existence of periodic solutions of population models modelled by ordinary differential equations and their discrete analogues in form of difference equations, and extension of these results to more general time scales are studied.…”

Section: Introductionmentioning

confidence: 99%

Impulsive Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on the Unification of Discrete and Continuous Systems

Güvenilir

Kaymakçalan²,

Pelen³

2015

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In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessary for the periodic solution of the predator-prey dynamic systems with Beddington-DeAngelis type functional response. For this study the main tools are time scales calculus and coincidence degree theory. Also the findings are beneficial for continuous case, discrete case and the unification of both these cases. Additionally, unification of continuous and discrete case is a good example for the modeling of the life cycle of insects.

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Periodic solutions for predator–prey systems with Beddington–DeAngelis functional response on time scales

Cited by 35 publications

References 8 publications

Existence of periodic solutions to a system with functional response on time scales

Existence of periodic solutions to a system with functional response on time scales

Nabla inequalities and permanence for a logistic integrodifferential equation on time scales

Impulsive Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on the Unification of Discrete and Continuous Systems

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