This paper is devoted to study the generalized synchronization of spatial chaotic systems by applying linear coupling. Based on the stability of the fixed point of a plane system, we obtain the stable domain of the space plane. According to the stable domain of the space plane, the stable domain of the coupling strength for the linear generalized synchronization of the spatial chaotic systems is determined. Moreover, the relationship between the stable fixed plane and the synchronization of the spatial chaos system is also analyzed. Finally, an example is presented to validate the scheme and the analysis.
This paper investigates behaviors that a set of initial cell densities of Heterocapsa Circularisquama (HC) and Prorocentrum Dentatum (PD) and a set of environmental factors disturbing the growth of HC and PD cells formed in their growth process, which are actually fractal phenomena. First, the calculation of the fractal dimension of the set of initial cell densities of HC and PD is given in the paper. Second, by controlling the set of initial cell density, HC and PD cells grow according to a given growth target. The approximate or same behaviors of two different sets of initial cell densities of HC and PD are realized by introducing the coupling terms. Finally, the set of environmental factors disturbing the growth of HC and PD cells is constructed by introducing real parameters. Then the result that makes HC and PD cells growing according to a given growth target is reached by a proper mathematical transform to the real parameters. The approximate or same behaviors of the set of environmental factors disturbing the growth of HC and PD cells are realized by introducing the coupling terms.
In this paper, the generalized synchronization and the inverse generalized synchronization of different dimensional spatial chaotic dynamical systems are studied. The generalized synchronization results have been derived using active control method and Lyapunov stability theory. Numerical simulations are performed to verify the effectiveness of the proposed schemes.
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