A Novel Megastable Hamiltonian System with Infinite Hyperbolic and Nonhyperbolic Equilibria

The dimension of the conservative chaotic systems is an integer and equals the system dimension, which brings about a better ergodic property and thus have potentials in engineering application than the dissipative systems. This paper investigates the phenomenon of megastability in a unique and simple conservative oscillator with infinite of hyperbolic and nonhyperbolic equilibria. Using traditional nonlinear analysis tools, we found that the introduced oscillator possesses an invariable energy and displays either self-excited or hidden dynamics depending on the stability of its equilibria. Besides, the conservative nature of the new system is validated using theoretical measurement. Furthermore, an analog simulator of the oscillator is built and simulated in the PSpice environment to confirm that the previous results were not artifacts.

The stationary distribution and ergodicity of a stochastic mutualism model

This paper is concerned with a stochastic mutualism system with toxicant substances and saturation terms. We obtain the sufficient conditions for the existence of a unique stationary distribution to the equation and it has an ergodic property. It is interesting and surprising that toxicant substances have no effect on the stationary distribution of the stochastic model. Simulations are also carried out to confirm our analytical results.

A note on the stationary distribution of stochastic SIS epidemic model with vaccination under regime switching

In this paper, the stochastic SIS epidemic model with vaccination under regime switching is further investigated. A new threshold Rs 0 which is different from that given in [22] is established. A new technique to deal with the nonlinear incidence and vaccination for stochastic epidemic model under regime switching is proposed. When Rs0 > 0, the existence of a unique stationary distribution and the ergodic property are obtained by constructing a new stochastic Lyapunov function with Markov switching. The corresponding result which is acquired in [22] is improved and extended.