New criteria on global asymptotic synchronization of Duffing-type oscillator system

In this paper, we are concerned with global asymptotic synchronization of Duffing-type oscillator system. Without using matrix measure theory, graph theory and LMI method, which are recently widely applied to investigating global exponential/asymptotic synchronization for dynamical systems and complex networks, four novel sufficient conditions on global asymptotic synchronization for above system are acquired on the basis of constant variation method, integral factor method and integral inequality skills.&nbsp

Blow-Up and Global Existence for a Degenerate Parabolic System with Nonlocal Sources

This paper investigates the blow-up and global existence of nonnegative solutions for a class of nonlocal degenerate parabolic system. By using the super- and subsolution techniques, the critical exponent of the system is determined. That is, if Pc=p1q1−(m−p2)(n−q2)<0, then every nonnegative solution is global, whereas if Pc>0, there are solutions that blowup and others that are global according to the size of initial values u0(x) and v0(x). When Pc=0, we show that if the domain is sufficiently small, every nonnegative solution is global while if the domain large enough that is, if it contains a sufficiently large ball, there is no global solution