In this paper we explore the existence of periodic solutions of a nonautonomous semi-ratio-dependent predator-prey dynamical system with functional responses on time scales. To illustrate the utility of this work, we should mention that, in our results this system with a large class of monotone functional responses, always has at least one periodic solution. For instance, this system with some ...

Denote x t x1 t , x2 t , . . . , xn t , xt x1t, x2t, . . . , xnt , xit s xi t s i 1, 2, . . . , n , s ∈ −τ, 0 , τ is a positive constant or τ ∞, the norm of a bounded continuous function space C −τ, 0 , R is defined as ‖φ‖ maxs∈ −τ,0 |φ s |, where |φ| max{|φi|, i 1, 2, . . . , n}, C −τ, 0 , R {φ ∈ C −τ, 0 , R : for all θ ∈ −τ, 0 , φ θ > 0}. We call an almost periodic function is positive if and...

The current article discusses the existence of monotonic discontinuous solutions for general nonlinear quadratic Volterra-Urysohn functional-integral equations in Orlicz spaces E? when function ? satisfies ?2-condition. case Lebesgue Lp (p > 1) are also examined. We use arguments measure noncompactness with Darbo fixed point theorem to prove our results.

In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical periodicity; in actual fact, observe that a remotely periodic function is nothing else but bounded, uniformly continuous quasi-asymptotically function. We introduce analyze several new classes $c$-almost functions ${\mathbb R}^{n},$ slowly oscillating further recently introduced class R}^{n}.$ provide certa...

Integrability and linearizability of the Lotka–Volterra systems are studied. We prove sufficient conditions for integrable but not linearizable systems for any rational resonance ratio. We give new sufficient conditions for linearizable Lotka–Volterra systems. Sufficient conditions for integrable Lotka–Volterra systems with 3 : q resonance are given. In the particular cases of 3 : 5 and 3 : 4 r...

We study a discrete host-parasitoid system where the host population follows the classical Ricker functional form and is also subject to Allee effects. We determine basins of attraction of the local attractors of the single population model when the host intrinsic growth rate is not large. In this situation, existence and local stability of the interior steady states for the host-parasitoid int...

This paper considers the optimal harvesting of a stochastic delay predator-prey model with Lévy jumps. The traditional optimal harvesting problem of this type of model is difficult because it is difficult to get the explicit solutions of the model or to solve the corresponding delay Fokker-Planck equation of the model. In this paper, we use an ergodic method to study this problem, and establish...

This paper considers the existence of positive almost-periodic solutions for almost-periodic LotkaVolterra cooperative system with time delay. By using Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost-periodic solutions are obtained. An example and its simulation figure are given to illustrate the effectiveness of our results.

In order to obtain the conditions for the existence of periodic and almost periodic solutions of Volterra difference equations, x(n+1) = f(n, x(n))+ ∑n s=−∞ F (n, s, x(n+ s), x(n)), we consider certain stability properties, which are referred to as (K, ρ)-weakly uniformly-asymptotic stability and (K, ρ)-uniformly asymptotic stability. Moreover, we discuss the relationship between the ρ-separati...

This paper is devoted to the existence of periodic solutions for a semi-ratio-dependent predatorprey system with time delays on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish necessary and sufficient conditions for the existence of periodic solutions. Our results show that for the most monotonic prey growth such as the logistic, the Gilpin,...