In this paper, we propose a stochastic ratio-dependent one-predator and two-mutualistic-preys model perturbed by white and telegraph noise. By the M-matrix analysis and Lyapunov functions, sufficient conditions of stochastic permanence and extinction are established. These conditions are all dependent on the parameters of subsystems and the stationary probability distribution of the Markov chain. We also obtain the boundary of limit superior and inferior of the average in time of the solution under stochastic permanence. Finally, we give two examples and numerical simulations to illustrate main results.

Linear feedback control and adaptive feedback control are proposed to achieve the synchronization of stochastic neutral-type memristive neural networks with mixed time-varying delays. By applying the stochastic differential inclusions theory, Lyapunov functional, and linear matrix inequalities method, we obtain some new adaptive synchronization criteria. A numerical example is given to illustrate the effectiveness of our results.

We propose a stochastic delayed one-predator and two-mutualistic-prey model perturbed by white noise and telegraph noise. By theM-matrix analysis and Lyapunov functions, sufficient conditions of stochastic permanence and extinction are established, respectively. These conditions are all dependent on the subsystems’ parameters and the stationary probability distribution of the Markov chain. We also investigate another asymptotic property and finally give two examples and numerical simulations to illustrate main results.