Global convergence of a class of networks on time scales

In this paper, we propose a class of simplified background neural networks model with two subnetworks on time scales. Some basic dynamic properties including positive invariance, boundedness, global attractivity and complete convergence of networks are analyzed. The main contributions in this paper are listed as follows: (1) the global attractive set of the model is verified and conditions for global attractivity are derived. (2) Complete convergence for the new networks are proved by constructing a novel energy function on time scales. Finally, three simulation examples are presented to illustrate the feasibility and effectiveness of the obtained results.

Bifurcation and attractor of the stochastic Rabinovich system with jump

In this paper, the bifurcation and attractor of the stochastic Rabinovich system with jump are discussed, and some new results for the system are presented. First, the sufficient condition and necessary condition for stochastic stability of the system are given. Second, the estimation of the global attractive set of system is obtained. The existence of random attractors of the stochastic Rabinovich system with jump is also discussed. Finally, stochastic bifurcation behavior for the system is analyzed. It is hoped that the investigation of this paper can help understanding the rich dynamic of the stochastic Rabinovich system and the true geometrical structure of the original amazing Rabinovich attractor.