We derived a stability criterion for the totally synchronized state of a periodic network of coupled functional units. The functional units were nonlinear discrete dynamical systems. We assumed exponentially decaying coupling strength to reduce the number of control parameters.

In this paper, we consider the prey-dependent consumption two-prey one-predator models with stage structure for the predator and impulsive effects. By applying the Floquet theory of linear periodic impulsive equation, we show that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value, that is, the pest populat...

there has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. the popular poincare-bendixon theorem applies well to the former but not the latter (see [2] and [3]). we give a necessary condition for the existence of periodic solutions for the third order autonomous systems, t...

We review recent experimental and theoretical studies on two-dimensional (2D) melting in the presence of a one-dimensional (1D) periodic potential. It is demonstrated that a colloidal suspension which is exposed to the interference pattern of two overlapping laser beams show a phase behaviour being totally different from that of 2D systems on homogeneous substrates. This is attributed to the ro...

Asymptotics and functional form of correlators in the XX-spin chain of finite length. Abstract We verify the functional form of the asymptotics of the spin-spin equal-time correlation function for the XX-chain, predicted by the hypothesis of conformal invariance at large distances and by the bosonization procedure. We point out that bosonization pocedure also predicts the functional form of the...