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Bifurcations in two coupled Rössler systems

Author

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  • Rasmussen, J.
  • Mosekilde, E.
  • Reick, C.

Abstract

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.

Suggested Citation

  • Rasmussen, J. & Mosekilde, E. & Reick, C., 1996. "Bifurcations in two coupled Rössler systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 40(3), pages 247-270.
    • Handle: RePEc:eee:matcom:v:40:y:1996:i:3:p:247-270
    DOI: 10.1016/0378-4754(95)00036-4
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