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Numerical studies of reaction–diffusion systems which consist of chaotic oscillators are carried out. The Rössler oscillators are used, which are arranged two–dimensionally and coupled by diffusion. Pacemakers where the average periods of the oscillators are artificially changed are set to produce target patterns. It is found that target patterns emerge from pacemakers and grow up as if they were in a regular oscillatory medium. The wavelength of the pattern can be varied and controlled by changing the parameters (size and frequency) of the pacemaker. The behavior of the coupled system depends on the size of the system and the strength of the pacemaker. When the system size is large, the Poincar
This article proposes a four dimensional autonomous hyperchaos generator whose nonlinear element is only one diode. The circuit is analyzed by regarding the diode as an ideal switch. Hence we can derive the two dimensional return map rigorously and its Lyapunov exponents confirm the hyperchaos generation. Also, a novel mathematical basis for the simplification to the ideal switch is given.