Positive periodic solutions in a discrete competitive system with the effect of toxic substances
نویسندگان
چکیده
In this paper, a delayed competitive system with the effect of toxic substances is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous non-autonomous delayed competitive system with the effect of toxic substances is proposed. By using Gaines and Mawhins continuation theorem of coincidence degree theory, a easily verifiable sufficient condition for the existence of positive solutions of difference equations is obtained. Keywords—competitive system; periodic solution; discrete time delay; topological degree
منابع مشابه
Periodic solutions in a delayed competitive system with the effect of toxic substances on time scales
In this paper, the existence of periodic solutions of a delayed competitive system with the effect of toxic substances is investigated by using the Gaines and Mawhins continuation theorem of coincidence degree theory on time scales. New sufficient conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the co...
متن کاملExtinction in two dimensional discrete Lotka-Volterra competitive system with the effect of toxic substances(II)
In this paper, we consider a two species non-autonomous discrete competitive phytoplankton system with one toxin producing phytoplankton. We show that for such kind of system, it is also possible one of the components be driven to extinction while the other one will be globally attractive with any positive solution of a discrete logistic equation under some conditions. Our results supplement th...
متن کاملPrey-Predator System; Having Stable Periodic Orbit
The study of differential equations is useful in to analyze the possible past or future with help of present information. In this paper, the behavior of solutions has been analyzed around the equilibrium points for Gause model. Finally, some results are worked out to exist the stable periodic orbit for mentioned predator-prey system.
متن کاملFour Positive Periodic Solutions of a Discrete Time Lotka-volterra Competitive System with Harvesting Terms
In this paper, by using Mawhin’s continuation theorem of coincidence degree theory, we establish the existence of at least four positive periodic solutions for a discrete time Lotka-Volterra competitive system with harvesting terms. An example is given to illustrate the effectiveness of our results.
متن کاملUniformly Asymptotic Stability of Positive Almost Periodic Solutions for a Discrete Competitive System
This paper is devoted to the study of almost periodic solutions of a discrete two-species competitive system. With the help of the methods of the Lyapunov function, some analysis techniques, and preliminary lemmas, we establish a criterion for the existence, uniqueness, and uniformly asymptotic stability of positive almost periodic solution of the system. Numerical simulations are presented to ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013