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Bistable traveling waves for monotone semiflows with applications

Jian Fang, Xiao-Qiang Zhao (2015)

Journal of the European Mathematical Society

This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. In an abstract setting, we establish the existence of traveling waves for discrete and continuous-time monotone semiflows in homogeneous and periodic habitats. The results are then extended to monotone semiflows with weak compactness. We also apply the theory to four classes of evolution systems.

Estimates for Principal Lyapunov Exponents: A Survey

Janusz Mierczyński (2014)

Nonautonomous Dynamical Systems

This is a survey of known results on estimating the principal Lyapunov exponent of a timedependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of ordinary differential equations and parabolic partial differential equations of second order. The estimates are given either in terms of the principal (dominant) eigenvalue of some derived time-independent equation or in terms of the parameters of the equation itself....

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