A stochastic predator-prey system with time-dependent delays is considered. Firstly, we show the existence of a global positive solution and stochastically ultimate boundedness. Secondly, the critical value between weak persistence and extinction of the prey is obtained and we also give the asymptotic pathwise estimation. Finally, we simulate the model to illustrate our results.

We propose a new stochastic competition chemostat system with saturated growth rate and impulsive toxicant input. The main purpose of this paper is to study the stochastic dynamics of a high-dimensional impulsive stochastic chemostat model and find the threshold between persistence and extinction for the impulsive stochastic chemostat system. First, we investigate the stability...

In this paper, a fractional-order model of palm trees, the lesser date moth and the predator is presented. Existence conditions of the local asymptotic stability of the equilibrium points of the fractional system are analyzed. We prove that the positive equilibrium point is globally stable also. The numerical simulations come to illustrate the dynamical behaviors of the model...

We propose and study a discrete competitive system of the following form: x 1 ( n + 1 ) = x 1 ( n ) exp [ r 1 − a 1 x 1 ( n ) − b 1 x 2 ( n ) 1 + c 2 x 2 ( n ) ] , x 2 ( n + 1 ) = x 2 ( n ) exp [ r 2 − a 2 x 2 ( n ) − b 2 x 1 ( n ) 1 + c 1 x 1 ( n ) ] . $$\begin{aligned} &x_{1}(n+1)=x_{1}(n)\exp{\biggl[r_{1}-a_{1}x_{1}(n)- \frac {b_{1}x_{2}(n)}{1+c_{2}x_{2}(n)}\biggr]}, \\ &x_{2...

The boundedness of chaotic systems plays an important role in investigating the stability of the equilibrium, estimating the Lyapunov dimension of attractors, the Hausdorff dimension of attractors, the existence of periodic solutions, chaos control, and chaos synchronization. However, as far as the authors know, there are only a few papers dealing with bounds of high-order...

Understanding the infectious diseases outbreak of algae can provide significant knowledge for disease control intervention and/or prevention. We consider here a disease caused by highly pathogenic organisms that can result in the death of algae. Even though a great deal of understanding about diseases of algae has been reached, studies concerning effects of the outbreak at the...

Using variational methods, we study the existence and multiplicity of homoclinic solutions for a class of discrete Schrödinger equations in infinite m-dimensional lattices with nonlinearities being superlinear at infinity. Our results generalize some existing results in the literature by using some weaker conditions.

In this paper we introduce the concept of a PC-mild solution to a general new class of noninstantaneous impulsive fractional differential inclusions involving the generalized Caputo derivative with the lower bound at zero in infinite dimensional Banach spaces. Using the formula of a PC-mild solution, we give two classes of sufficient conditions to guarantee the existence of PC...

In this article, we propose an exponential B-spline approach to obtain approximate solutions for the fractional sub-diffusion equation of Caputo type. The presented method is established via a uniform nodal collocation strategy by using an exponential B-spline based interpolation in conjunction with an effective finite difference scheme in time. The unique solvability is...

In this paper, we study a coupled system of fractional boundary value problems subject to integral boundary conditions. By applying a recent fixed point theorem in ordered Banach spaces, we investigate the local existence and uniqueness of positive solutions for the coupled system. We show that the unique positive solution can be found in a product set, and that it can be...

The equivalent integral equation of a new form for a class of fractional evolution equations is obtained by the method of Laplace transform, which is different from those given in the existing literature. By the monotone iterative method without the assumption of lower and upper solutions, we present some new results on the existence of positive mild solutions for the abstract...

We discuss the numerical solution of the time-fractional telegraph equation. The main purpose of this work is to construct and analyze stable and high-order scheme for solving the time-fractional telegraph equation efficiently. The proposed method is based on a generalized finite difference scheme in time and Legendre spectral Galerkin method in space. Stability and convergence...

A mathematical model of Dengue virus transmission between mosquitoes and humans, incorporating a control strategy of imperfect vaccination and vector maturation delay, is proposed in this paper. By using some analytical skills, we obtain the threshold conditions for the global attractiveness of two disease-free equilibria and prove the existence of a positive equilibrium for this...

In this paper, an effective numerical method to solve the Cauchy type singular Fredholm integral equations (CSFIEs) of the first kind is proposed. The collocation technique based on Bernstein polynomials is used for approximation the solution of various cases of CSFIEs. By transforming the problem into systems of linear algebraic equations, we see that this approach is...

This paper is concerned with the oscillatory behavior of first-order retarded [advanced] difference equation of the form Δ x ( n ) + p ( n ) x ( τ ( n ) ) = 0 , n ∈ N 0 [ ∇ x ( n ) − q ( n ) x ( σ ( n ) ) = 0 , n ∈ N ] , where ( p ( n ) ) n ≥ 0 [ ( q ( n ) ) n ≥ 1 ] is a sequence of nonnegative real numbers and τ ( n ) [ σ ( n ) ] is a non-monotone sequence of integers such that...

In this paper, we study anti-periodic boundary value problems for systems of generalized Sturm-Liouville and Langevin fractional differential equations. Existence and uniqueness results are proved via fixed point theorems. Examples illustrating the obtained results are also presented. MSC: 34A08, 34A12, 34B15.

The goal of this paper is to study the stability and traveling waves of stage-structured predator-prey reaction-diffusion systems of Beddington-DeAngelis functional response with both nonlocal delays and harvesting. By analyzing the corresponding characteristic equations, the local stability of various equilibria is discussed. We reduce the existence of traveling waves to the...

In this paper, a general neutral stochastic functional differential equations with infinite delay and Lévy jumps (NSFDEwLJs) is studied. We investigate the existence and uniqueness of solutions to NSFDEwLJs at the phase space C g under the local Carathéodory type conditions. Meanwhile, we also give the exponential estimates and almost surely asymptotic estimates of solutions to...

In this paper, the existence of local and global Hopf bifurcation for a delay commodity market model is studied in detail. As time delay increases, the commodity price will fluctuate periodically. Furthermore, such fluctuations will occur even if the time delay is sufficiently large. MSC: 91B55, 34K18.

This paper is concerned with fuzzy bidirectional associative memory (BAM) Cohen-Grossberg neural networks with mixed delays and impulses. By constructing an appropriate Lyapunov function and a new differential inequality, we obtain some sufficient conditions which ensure the existence and global exponential stability of a periodic solution of the model. The results in this paper...

We study the nonexistence of (nontrivial) global solutions for a class of fractional integro-differential problems in an appropriate underlying space. Integral conditions on the kernel, and for some degrees of the involved parameters, ensuring the nonexistence of global solutions are determined. Unlike the existing results, the source term considered is, in general, a convolution...

This paper investigates the long time behavior of tumor cells evolution in a tumor-immune system competition model perturbed by environmental noise. Sufficient conditions for extinction, stochastic persistence, and strong persistence in the mean of tumor cells are derived by constructing Lyapunov functions. The study results show that environmental noise can accelerate the...

The purpose of this paper is to study solvability of the higher order nonlinear neutral delay differential equation d n d t n [ x ( t ) + c ( t ) x ( t − τ ) ] + ( − 1 ) n + 1 f ( t , x ( σ 1 ( t ) ) , x ( σ 2 ( t ) ) , … , x ( σ k ( t ) ) ) = g ( t ) , t ≥ t 0 , where n and k are positive integers, τ > 0 , t 0 ∈ R , f ∈ C ( [ t 0 , + ∞ ) × R k , R ) , c , g , σ i ∈ C ( [ t 0...

In this paper, we study a class of nonlinear multiple base points impulsive fractional differential equations involving the three-point boundary conditions. A new result on the existence of a solution is established by using fixed point theorems. An example is presented to illustrate the result. MSC: 34A08, 34A37, 34B10.

The paper develops a derivative-type (D-type) networked iterative learning control (NILC) scheme for repetitive discrete-time systems with packet dropouts stochastically occurred in input and output communication channels. The scheme generates the sequential recursive-mode control inputs by mending the dropped instant-wise output with the synchronous desired output, while it...