This paper is devoted to studying the stability of unique equilibrium point and occurrence Hopf bifurcation as well limit cycles a three-dimensional chaotic system. We characterize parameters for which takes place at point. In addition, system has only one . It was proved that  is asymptotically stable unstable when  and , respectively. Moreover, cyclicity system, two techniques are u...

Short time existence for a surface diffusion evolution equation with curvature regularization is proved in the context of epitaxially strained three-dimensional films. This is achieved by implementing a minimizing movement scheme, which is hinged on the H−1-gradient flow structure underpinning the evolution law. Long-time behavior and Liapunov stability in the case of initial data close to a fl...

In this paper, the results of Freedman and So (1985) on global stability and persistence of simple food chains are extended to general diffusive food chains. For global stability of the unique homogeneous positive steady state, our approach involves an application of the invariance principle of reaction-diffusion equations and the construction of a Liapunov functional. For persistence, we use t...

(2) C(t, s) ≥ 0, Cs(t, s) ≥ 0, Cst(t, s) ≤ 0, Ct(t, s) ≤ 0. The subscripts denote the usual partial derivatives and a is continuous. Convex kernels for both integral and integrodifferential equations are commonly used in the study of many real-world problems. Discussions may be found in Volterra [13], Grippenberg-Londen-Staffans [7; see index], Londen [10], and throughout Burton [4], for exampl...