Abstract
In this paper, we will prove that the local RDS φ generated by the stochastic logistic equation with non-Gaussian Lévy noise is continuous, linear and crude cocycle by basing on multiplicative ergodic theorem. Then we determine all invariant measures of the local RDS φ generated by the stochastic logistic equation with non-Gaussian Lévy noise, and we calculate the Lyapunov exponent for each of these measures. Furthermore, we will show that the stochastic logistic equation with non-Gaussian Lévy noise admits a D-bifurcations which is significantly different from the classical Brownian motion process.
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