No abstract

Because the two-dimensional coupled ecosystem has perfect symmetry, the dynamical behavior of symmetric dynamical system is discussed. The analysis of the dynamical behavior of a two-dimensional coupled ecosystem with stochastic parameters is explored in this paper. Firstly, a two-dimensional coupled ecosystem with stochastic parameters is established, it is transformed into a deterministic equivalent system by orthogonal polynomial approximation. Then, analysis of the dynamical behaviour of equivalently deterministic coupled ecosystems is performed using stability theory. At last, we analyzed the dynamical behaviour of non-trivial points by means of the mathematics analysis method and found the influence of random parameters on asymptotic stability in coupled ecosystem is prominent. The dynamical behaviour analysis results were verified by numerical simulation.

No abstract

This paper investigates stochastic differential equations (SDEs) with locally one-sided Lipschitz coefficients. Apart from the local one-sided Lipschitz condition, a more general condition is introduced to replace the monotone condition. Then, in terms of the Euler’s polygonal line method, the existence and uniqueness of solutions for SDEs is established. In the meanwhile, the $p$th moment boundedness of solutions is also provided.