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This article concerns Liénard-type systems with time-varying de-lays. By applying the theory of exponential dichotomies, the properties of pseudo almost periodic function, inequality analysis techniques, and contrac tion mapping principle, new criteria for the existence and uniqueness of pseudo almost periodic solutions are established. An example is given to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper is concerned with cellular neural networks with proportional delays. The proportional delay is a time-varying unbounded delay which is different from the constant delay, bounded time-varying delay and distributed delay. Using matrix measure and generalized Halanay inequality, some sufficient conditions are obtained to ensure the pth exponential stability of cellular neural networks with proportional delays. The obtained results are simple and easy to be verified. An example is given to illustrate the effectiveness of the obtained results. This paper ends with a brief conclusion. [ABSTRACT FROM AUTHOR]

In this paper, a neutral multi-species logarithmic population model is investigated. By applying the matrix's spectral theory which is different from the methods employed in the literature, a set of sufficient conditions are obtained for the existence and uniqueness of almost periodic solution of the neutral multi-species logarithmic population model. The obtained sufficient conditions are given in terms of spectral radius of explicit matrices which are much different from those by the algebraic inequalities. An example is given to illustrate the feasibility and effectiveness of the obtained results. The results of this paper are completely new and generalize those of the previous studies. [ABSTRACT FROM AUTHOR]

In this article we study a cellular neural network with impulsive effects. By using differential inequality techniques, we obtain verifiable crite- ria on the existence and exponential stability of anti-periodic solutions. An example is included to illustrate the feasibility and of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we study an Nicholson-type delay system with delays. New criteria for the boundedness and exponential stability of positive solutions of Nicholson-type system with time-varying delays are established by applying the fundamental solution matrix, inequality techniques and Lyapunov method. Two examples with their computer simulations are presented to illustrate the effectiveness of the theoretical findings. Our results are new and supplement some previously known ones. [ABSTRACT FROM AUTHOR]

This paper deals with a delayed three-level food chain model with Beddington-DeAngelis functional response. By using the differential inequality theory, a set of sufficient conditions are obtained for the permanence of the system. By constructing a suitable Liapunov function, we derive that the system has a unique asymptotically periodic solution which is globally asymptotically stable. An example is given to illustrate the effectiveness of the results. The paper ends with a brief conclusion. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate the problem of controlling chaos in a 3D ratio-dependent food chain system. Time-delayed feedback control method is applied to suppress chaos to unstable equilibria or unstable periodic orbits. By local stability analysis, we theoretically prove the occurrences of Hopf bifurcation. Some numerical simulations are presented to support theoretical predictions. Finally, main conclusions are drawn. [ABSTRACT FROM AUTHOR]

A periodic discrete time three species competition system is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous nonautonomous three species competition system is proposed. By using Gaines and Mawhin's continuation theoremof coincidence degree theory, sufficient conditions for the existence of positive periodic solutions of the model are obtained. [ABSTRACT FROM AUTHOR]

A ratio-dependent predator-prey model with two delays is investigated. The conditions which ensure the local stability and the existence of Hopf bifurcation at the positive equilibrium of the systemare obtained. It shows that the two different time delays have different effects on the dynamical behavior of the system. An example together with its numerical simulations shows the feasibility of the main results. Finally, main conclusions are included. [ABSTRACT FROM AUTHOR]

A Lotka-Volterra predator-prey model with time-varying delays is investigated. By using the differential inequality theory, some sufficient conditions which ensure the permanence and global asymptotic stability of the system are established. The paper ends with some interesting numerical simulations that illustrate our analytical predictions. [ABSTRACT FROM AUTHOR]

We propose and deal with a discrete mutualism model with infinite deviating arguments and feedback controls. Sufficient conditions which guarantee the permanence of the system are obtained by using the difference inequality theory. The paper ends with brief conclusions. [ABSTRACT FROM AUTHOR]

An asymptotically periodic predator-prey model with time delay is investigated. Some sufficient conditions for the uniformly strong persistence of the system are obtained. Our result is an important complementarity to the earlier results. [ABSTRACT FROM AUTHOR]

Adelayed predator-preymodel with disease in the prey is investigated. The conditions for the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are derived. The effect of the two different time delays on the dynamical behavior has been given. Numerical simulations are performed to illustrate the theoretical analysis. Finally, the main conclusions are drawn. [ABSTRACT FROM AUTHOR]

A delayed neural network model of two neurons with inertial coupling is dealt with in this paper. The stability is investigated and Hopf bifurcation is demonstrated. Applying the normal form theory and the center manifold argument, we derive the explicit formulas for determining the properties of the bifurcating periodic solutions. An illustrative example is given to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

A class of discrete-time system modelling a network with two neurons is considered. First, we investigate the global stability of the given system. Next, we study the local stability by techniques developed by Kuznetsov to discrete-time systems. It is found that Neimark-Sacker bifurcation (or Hopf bifurcation for map) will occur when the bifurcation parameter exceeds a critical value. A formula determining the direction and stability of Neimark-Sacker bifurcation by applying normal form theory and center manifold theorem is given. Finally, some numerical simulations for justifying the theoretical results are also provided. [ABSTRACT FROM AUTHOR]

By using Schaeffer's theorem and Lyapunov functional, sufficient conditions of the existence and globally exponential stability of positive periodic solution to an impulsive neural network with time-varying delays are established. Applications, examples, and numerical analysis are given to illustrate the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

A class of stage-structured predator-prey model with time delay and delay-dependent parameters is considered. Its linear stability is investigated and Hopf bifurcation is demonstrated. Using normal form theory and center manifold theory, some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained. Finally, numerical simulations are performed to verify the analytical results. [ABSTRACT FROM AUTHOR]

A class of Beddington-DeAngelis functional response predator-prey model is considered. The conditions for the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are derived. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, main conclusions are given. [ABSTRACT FROM AUTHOR]

In this paper, a special SEIR epidemic model with nonlinear incidence rates is considered. By analyzing the associated characteristic transcendental equation, it is found that Hopf bifurcation occurs when these delays pass through a sequence of critical value. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation for justifying the theoretical analysis are also presented. Finally, biological explanations and main conclusions are given. [ABSTRACT FROM AUTHOR]

Applying a frequency domain approach, we investigate a phytoplankton model with time delay. We use the delay as a bifurcation parameter; as it passes through a sequence of critical values, Hopf bifurcation occurs. A family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulations illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

A discrete predator-prey model with Holling II and Beddington-DeAngelis functional responses is investigated. With the aid of differential equations with piecewise constant arguments, a discrete version of continuous nonautonomous delayed predator-prey model with Beddington- DeAngelis functional responses is proposed. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive solutions of the model are established. [ABSTRACT FROM AUTHOR]

A class of two-neuron networks with resonant bilinear terms is considered. The stability of the zero equilibrium and existence of Hopf bifurcation is studied. It is shown that the zero equilibrium is locally asymptotically stable when the time delay is small enough, while change of stability of the zero equilibrium will cause a bifurcating periodic solution as the time delay passes through a sequence of critical values. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Finally, numerical simulations supporting the theoretical analysis are carried out. [ABSTRACT FROM AUTHOR]

This paper studies the global asymptotic stability for positive solutions to the higher order rational difference equation xn = Π mj=1(xn-kj + 1) + Π mj=1(xn-kj - 1))/(Π mj=1(xn-kj + 1) - Π mj=1(xn-kj - 1)) n = 0, 1, 2, . . ., where m is odd and x-km, x-km+1, . . . , x-1 ∈. (0, ∞). Our main result generalizes several others in the recent literature and confirms a conjecture by Berenhaut et al., 2007. [ABSTRACT FROM AUTHOR]