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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 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]

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]