Integer multiple spiking induced by Gaussian white noise in the stochastic Chay system may occur near a subcritical Hopf bifurcation of the corresponding deterministic system without external periodic forcing. The deterministic Chay system near the subcritical Hopf bifurcation can exhibit a damped subthreshold oscillation of membrane potential, and can easily fire a spike in response to some kinds of weak pulses. Therefore, on account of the characteristic of Gaussian white noise, it can be shown that the deterministic Chay system supplied with certain weak pulses can fire integer multiple spiking similar to that in the corresponding stochastic system. Furthermore, on the light of the characteristic of the unstable limit cycle "before" a subcritical Hopf bifurcation in the deterministic Chay model, it can be explained that integer multiple spiking only appears in a certain range of the parameter VK.

In this paper, some suffcient conditions under which the quasilinear elliptic system −div(|∇u|p−2∇u)=um1vn1;−div(|∇u|q−2∇u) =um2vn2 in RN (N¿3) has no radially symmetric positive solution is derived. Then by using this non-existence result, blow-up estimates for a class of quasilinear reaction-diffusion systems ut=div(|∇u|p−2∇u)+um1vn1; vt=div(|∇v|q−2∇v)+um2vn2 with the homogeneous Dirichlet boundary value conditions are obtained. Copyright ? 2003 John Wiley & Sons, Ltd.

The prior estimate and decaypropertyof positive solutions are derived for a system of quasilinear elliptic diserential equations 3rst. Then, the nonexistence result for radiallynonincreasing positive solutions of the sys11 tem is implied. Byusing this nonexistence result, blow-up estimates for a class of quasilinear reaction-diffusion systems (non-Newtonian 3ltration systems) are established to extend the result for semilinear reaction-disusion 13 systems (Fujita type).

A new qualitative method is presented for studying the bifurcation problems of nonlinear systems with time-dependent parameters. The concept of stability on nite time intervals is introduced and some related stability theorems are established in order to analyze time-dependent bifurcation problems. As some applications of the new method, three dierent types of delayed bifurcation transitions and jump phenomena of time-dependent Dungvan der Polse quation are investigated qualitatively. The bifurcation transition values are predicted by constructing the V-functions or by the linear stability. The sensitivity of motion to the initial values and parameters is also discussed.

This paper deals with grazing rub-impact dynamics in a rotor system by using the rub-impact Poincar

A period adding bursting sequence without bursting-chaos in the Chay neuron model is studied by bifurcation analysis. The gent, sis of each periodic bursting is separately evoked by thc corrcsponding periodic spiking patterns through two period doubling bifurcations, except for the period-1 bursting occurring via Hopf bifurcation. Hence, it is concluded that this period adding bursting bifhrcation without chaos has a compound bifurcation structure closely related to pcriod-doubling bifurcations of periodic spiking in essence.

Complete synchronization of coupled Hindmarsh Rope (HR) neurons with a ring structure is studied. The criterion for complete synchronization of coupled neurons with the ring structure is obtained through the stability analysis of the iincarizcd synchronization error system, Numerical simulation is given to test the critcrion for a system with three coupled HR neurons.

The firing activities of Hindmarsh-Rose (HR) neurons are studied by means of numerical simulation and bifurcation analysis. A single HR neuron exhibits various firing patterns, such as quiescent state, periodic spiking, periodic bursting and chaos, when the external current input is changed. The fast/slow dynamical analysis is applied to explore the dynamical behaviour of the HR model. The complete synchronization of two coupled identical HR neurons with electrical coupling mimicking gap junctions can be realized in certain ranges of the coupling strength, whenever each individual neuron shows quiescency, periodic firing and chaos. The criteria for complete synchronization are analysed theoretically, and the corresponding numerical simulation is presented as well. The persistence of the interspike intervals bifurcation structure of the coupled HR neuronal system under electrical coupling is also discussed.