TY - JOUR

T1 - Forcing an entire bifurcation diagram

T2 - Case studies in chemical oscillators

AU - Kevrekidis, I. G.

AU - Aris, R.

AU - Schmidt, L. D.

N1 - Funding Information:
This work was partiallys upportebdy NSF grant no. CPE 83-13497a nd the U.S. Departmenot f Energy.

PY - 1986/12

Y1 - 1986/12

N2 - 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of the autonomous bifurcation diagram so that the characterization of the system as a simple forced oscillator is no longer valid.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.

AB - 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of the autonomous bifurcation diagram so that the characterization of the system as a simple forced oscillator is no longer valid.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.

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U2 - 10.1016/0167-2789(86)90145-4

DO - 10.1016/0167-2789(86)90145-4

M3 - Article

AN - SCOPUS:0000573221

VL - 23

SP - 391

EP - 395

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-3

ER -