Abstract
This paper discusses the Lorenz–Stenflo system under the influence of L\(\acute{\hbox {e}}\)vy noise. We find conditions under which the solution to stochastic Lorenz–Stenflo system is exponentially stable. We then investigate the estimation of the global attractive set and stochastic bifurcation behavior of the stochastic Lorenz–Stenflo system. Results show that the jump noise can make the solution stable, the bounds and bifurcation to undergo change under some conditions. Numerical results show the effectiveness and advantage of our methods.
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