Cellular Neural Networks And Chaotic Dynamics Of Incompressible Elastomers

In this thesis,we study the chaotic dynamics of RTD-based cellular neural network (RTD-CNN for short)and a pre-stressed incompressible elastic plate due to resonanttriad interactions.There are two parts:the first one is about chaos and hyperchaos of RTD-CNN,the second is concerning with chaotic motion and Hamiltonian dynamics of a pre-stressed incompressible elastic plate.In the first part,with the help of "snap-back repeller" and Marotto theorem,we obtained that the discrete RTD-CNN exhibit chaotic dynamics in the Li-Yorke sense. Moreover,with the help of symbolic dynamics and horseshoes,we also proved that the discrete RTD-CNN is semi-conjugate to the shift map of the three symbol space(∑₃,σ). Therefore,under suitable conditions,the RTD-based CNN is chaotic.Computer simulation results of system's bifurcation and phase portrait demonstrate these chaotic dynamics.Similar to three routes to chaos,three routes to hyperchaos is given out in our thesis. A rigorous analysis for the later two routes is performed.About the second route,under Oseledec multiple ergodic theory,we find two directions in which Lyapunov exponents are positive.That is to say the system will exhibits hyperchaotic dynamics.The bifurcation diagram and Lyapunov exponents spectrum demonstrate these hyperchaotic phenomenon. The third route is explained as the result of absorption,that is compound-saddle point absorbs compound-node point.From phase portrait we can see the existence of scroll motion and bond motion simultaneously.The novelty of this part is the mechanism of chaos-hyperchaos transition.The application of chaos and hyperchaos in communication is put in the fourth chapter of our thesis.In the second part,we analyze amplitude equations of a pre-stressed incompressible elastic plate using dynamical systems theory.Regions of the parametric space that correspond to bounded solutions are determined and some explicit representations of the bounded solutions are obtained.It is shown that the resonant-triad interaction can lead to chaotic motions.In the last of our thesis,some proposals and prospects are presented.