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【期刊论文】Blow-up estimates for a quasi-linear reaction-diffusion system
陆启韶, Yang Zuodong* and Lu Qishao, Communicated by G. F. Roach
Math. Meth. Appl. Sci. 2003; 26:1005-1023,-0001,():
-1年11月30日
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.
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陆启韶, Zuodong Yang, Qishao Lu*
,-0001,():
-1年11月30日
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).
Blow-up, Quasilinear reaction-diffusion system, Positive radial solutions, Existence and nonexistence
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【期刊论文】TIME-DEPENDENT BIFURCATION: A NEW METHOD AND APPLICATIONS
陆启韶, CUN-CAI HUA and QI-SHAO LU*
International Journal of Bifurcation and Chaos, Vol. 11, No.12(2001)3153-3162,-0001,():
-1年11月30日
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.
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【期刊论文】Characteristics of Period-Adding Bursting Bifurcation Without Chaos in the Chay Neuron Model*
陆启韶, YANG Zhuo-Qin, , LUQi-Shao, *
Vol. 21, No.11(2004)2124,-0001,():
-1年11月30日
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.
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【期刊论文】Complete Synchronization of Coupled Hindmarsh-Rose Neurons with Ring Structure*
陆启韶, SHI Xia, LU Qi-Shao*, *
Vol. 21, No.9(2004)1695,-0001,():
-1年11月30日
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.
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