Forcing an entire bifurcation diagram: Case studies in chemical oscillators

I. G. Kevrekidis, R. Aris, L. D. Schmidt

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We study the finite amplitude periodic forcing of chemical oscillators. In particular, we examine systems that, when autonomous, (i.e. for zero forcing amplitude) exhibit a single stable oscillation. Using one of the system parameters as a forcing variable by varying it periodically, we show through extensive numerical work how the bifurcation diagram of the autonomous system with respect to this parameter affects the qualitative response of the full forced system. As the forcing variable oscillates around its midpoint, its instantaneous values may cross points (such as Hopf bifurcation poiints) of the autonomous bifurcation diagram so that the characterization of the system as a simple forced oscillator is no longer valid. Such a neighboring Hopf bifurcation of the unforced system is found to set the scene for the interaction of resonance horns and the loss of tori in the full forced system as the amplitude of the forcing grows. Our test case presented here is the Continuous Stirred Tank Reactor (CSTR) with periodically forced coolant temperature.

Original languageEnglish (US)
Pages (from-to)391-395
Number of pages5
JournalPhysica D: Nonlinear Phenomena
Issue number1-3
StatePublished - Dec 1986

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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