Occurrence of regular, chaotic and hyperchaotic behavior in a family of modified Rossler hyperchaotic systems

Abstract In this paper, we demonstrate that it is possible to control the hyperchaos into the Rossler hyperchaotic system (RHS) by linear feedback of own signals. After introducing of the parameter “ b ” in the z -equation ( b → b + b 1 x ( t )+ b 2 y ( t )+ b 3 z ( t )+ b 4 w ( t )), we study how the global dynamics can be altered in a desired direction ( b n are considered as free parameters). We make a detailed bifurcation investigation of the modified Rossler hyperchaotic systems by varying the parameters b n . Finally, we calculate the Lyapunov exponents and the information dimension, where the regular, chaotic and hyperchaotic motion of modified RHS exist.

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