We consider a system of differential equations the behavior of which solutions possesses several properties characteristic of the blood pressure distribution. The system can be used for a compartmental modeling [8, 15] of the cardiovascular system. It admits a unique bounded solution such that all coordinates of the solution are separated from zero by positive numbers, and which is periodic, ev...

In this paper we will consider the nonlinear impulsive delay host–macroparasite model with periodic coefficients. By means of the continuation theorem of coincidence degree, we establish a sufficient condition for the existence of a positive periodic solution M(t) with strictly positive components. Moreover, we establish a sufficient condition for the global attractivity of M(t) and some suffic...

This article concerns the stability and periodicity of solutions to the delay dynamic system x4(t) = A(t)x(t) + F (t, x(t), x(g(t))) + C(t) on a time scale. By the inequality technique for vectors, we obtain some stability criteria for the above system. Then, using the Horn fixed point theorem, we present some conditions under which our system is asymptotically periodic and its periodic solutio...

In this paper, a class of recurrent neural networks (RNNs) with variable delays are studied on almost periodic time scales, some sufficient conditions are established for the existence and global exponential stability of the almost periodic solution. These results have important leading significance in designs and applications of RNNs. Finally, two examples and numerical simulations are present...

In this paper, we study the nonnegative periodic dynamics of the delayed Cohen–Grossberg neural networks with discontinuous activation functions and periodic interconnection coefficients, selfinhibitions, and external inputs. Filippov theory is utilized to study the viability, namely, the existence of the solution of the Cauchy problem. Under some conditions, the existence and the asymptotical ...

In this work, we study the existence of periodic solutions for partial neutral functional differential equation. We assume that the linear part is not necessarily densely defined and satisfies the Hille-Yosida condition. In the nonhomogeneous linear case, we prove that the existence of a bounded solution on R+ implies the existence of a periodic solution. In nonlinear case, we use the concept o...

According to the integrated pest management strategies, we propose a model for pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one periodic solution of such system, and further, the attractiveness of the order one periodic solution by sequence conver...

⎯In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improv...