Abstract: In this paper, we consider the almost periodic solutions of a discrete cooperation system with feedback controls. Assuming that the coefficients in the system are almost periodic sequences, we obtain the existence and uniqueness of the almost periodic solution which is uniformly asymptotically stable.
Abstract: In this paper zero-dissipative explicit Runge-Kutta
method is derived for solving second-order ordinary differential
equations with periodical solutions. The phase-lag and dissipation
properties for Runge-Kutta (RK) method are also discussed. The new
method has algebraic order three with dissipation of order infinity.
The numerical results for the new method are compared with existing
method when solving the second-order differential equations with
periodic solutions using constant step size.
Abstract: In this paper, by utilizing the coincidence degree theorem a predator-prey model with modified Leslie-Gower Hollingtype II schemes and a deviating argument is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions of the model.
Abstract: This paper deals with a delayed single population model on time scales. With the assistance of coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Furthermore, the better estimations for bounds of periodic solutions are established.
Abstract: In this paper, by applying Mawhin-s continuation theorem of coincidence degree theory, we study the existence of almost periodic solutions for neural multi-delay logarithmic population model and obtain one sufficient condition for the existence of positive almost periodic solution for the above equation. An example is employed to illustrate our result.
Abstract: 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 presented to illustrate the feasibility and effectiveness of the results.
Abstract: In this paper, by using the continuation theorem of coincidence degree theory, M-matrix theory and constructing some suitable Lyapunov functions, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of recurrent neural networks with distributed delays and impulses on time scales. Without assuming the boundedness of the activation functions gj, hj , these results are less restrictive than those given in the earlier references.
Abstract: This paper is concerned with an epidemic model with delay. By using the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, Some sufficient conditions which guarantee the permeance and existence of a unique globally attractive positive almost periodic solution of the model are obtain. Finally, an example is employed to illustrate our result.
Abstract: In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.
Abstract: By using Mawhin-s continuation theorem of coincidence degree theory, we establish the existence of 2n positive periodic solutions for n species non-autonomous Lotka-Volterra competition systems with harvesting terms. An example is given to illustrate the effectiveness of our results.
Abstract: By using the method of coincidence degree theory and constructing suitable Lyapunov functional, several sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for Cohen-Grossberg shunting inhibitory neural networks with delays. An example is given to illustrate our feasible results.
Abstract: This paper is devoted to a delayed periodic predatorprey system with non-monotonic numerical response on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of multiple periodic solutions. As corollaries, some applications are listed. In particular, our results improve and generalize some known ones.
Abstract: In this paper, based on the estimation of the Cauchy matrix of linear impulsive differential equations, by using Banach fixed point theorem and Gronwall-Bellman-s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays and impulses. An example is given to illustrate the main results.
Abstract: In this paper, a delayed physiological control system is investigated. The sufficient conditions for stability of positive equilibrium and existence of local Hopf bifurcation are derived. Furthermore, global existence of periodic solutions is established by using the global Hopf bifurcation theory. Finally, numerical examples are given to support the theoretical analysis.
Abstract: The dynamics of a delayed mathematical model for
Hes1 oscillatory expression are investigated. The linear stability of
positive equilibrium and existence of local Hopf bifurcation are
studied. Moreover, the global existence of large periodic solutions
has been established due to the global bifurcation theorem.
Abstract: With the help of coincidence degree theory, sufficient
conditions for existence of periodic solutions for a food chain model
with functional responses on time scales are established.
Abstract: A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results. Based on the global Hopf bifurcation theorem for general functional differential equations, the global existence of periodic solutions is established.
Abstract: In this paper, a delayed prototype model is studied. Regarding the delay as a bifurcation parameter, we prove that a sequence of Hopf bifurcations will occur at the positive equilibrium when the delay increases. Using the normal form method and center manifold theory, some explicit formulae are worked out for determining the stability and the direction of the bifurcated periodic solutions. Finally, Computer simulations are carried out to explain some mathematical conclusions.
Abstract: In this paper, by employing a new Lyapunov functional
and an elementary inequality analysis technique, some sufficient
conditions are derived to ensure the existence and uniqueness of
periodic oscillatory solution for fuzzy bi-directional memory (BAM)
neural networks with time-varying delays, and all other solutions of
the fuzzy BAM neural networks converge the uniqueness periodic
solution. These criteria are presented in terms of system parameters
and have important leading significance in the design and applications
of neural networks. Moreover an example is given to illustrate the
effectiveness and feasible of results obtained.
Abstract: This paper is concerned with the existence and unique¬ness of pseudo-almost periodic solutions to the chaotic delayed neural networks (t)= —Dx(t) ± A f (x (t)) B f (x (t — r)) C f (x(p))dp J (t) . t-o Under some suitable assumptions on A, B, C, D, J and f, the existence and uniqueness of a pseudo-almost periodic solution to equation above is obtained. The results of this paper are new and they complement previously known results.