Bifurcations in two coupled Rössler systems Original Research Article

This paper presents a bifurcation analysis of two symmetrically coupled Rössler systems. The assumed symmetry does not allow any one direction to become preferred, and the coupled system is therefore an example of a higher-dimensional dissipative system which does not become effectively one-dimensional. The results are presented in terms of one- and two-parameter bifurcation diagrams. A particularly interesting finding is the replacement of some of the period-doubling bifurcations by torus bifurcations with the result that instead of the Feigenbaum transition to chaos a quasiperiodic scenario with frequency locking occurs. Calculation of the largest Lyapunov exponents reveals that the system is hyperchaotic in a significant fraction of parameter space.