Abstract
The qualitative theory of nonlinear spatial dynamical systems has attracted increasing attention recently. In particular, we have studied construction of spatial periodic orbits, dynamical behaviors of spatial chaos in the sense of Li–Yorke–Marotto, spatial Lyapunov exponents, control and generalized synchronization of spatial chaotic systems. In this paper, we apply a special mathematical transform to obtain spatial chaos on surface and its associated bifurcation and Feigenbaum problem. The 2D Logistic system is used for illustration. In addition, we also illustrate the difference in essence about chaos on surface as high-dimensional spatial system and dimension in phase space and we also analyze the parallel and different characters of theory system between 1D and 2D Logistic system.
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