Experiments on bifurcations to chaos in a forced chemical reactor

Abstract Oscillations and bifurcations to chaos are studied experimentally in a forced, isothermal, continuous stirred reactor. The forcing is produced by varying the concentration of a feed species of the Belousov-Zhabotinskii reaction. The behaviour of the system is studied as a function of two parameters, the period and amplitude of the forcing, and variations in either are shown to lead to period doubling bifurcations to chaos. By using Fourier transforms and Poincare sections we show how the behaviour varies throughout the chaotic region.

[1]  R. M. Noyes,et al.  Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction , 1974 .

[2]  James E. Bailey,et al.  Pat-hological dynamic behavior of forced periodic chemical processes , 1977 .

[3]  M. Marek Periodic and Aperiodic Regimes in Forced Chemical Oscillations , 1985 .

[4]  K. Tomita,et al.  Chaotic response of a limit cycle , 1979 .

[5]  J. L. Hudson,et al.  Oscillatory and chaotic behaviour of a forced exothermic chemical reaction , 1984 .

[6]  J. L. Hudson,et al.  An experimental study of multiple peak periodic and nonperiodic oscillations in the Belousov–Zhabotinskii reaction , 1979 .

[7]  Masakazu Matsubara,et al.  BIFURCATIONS AND CHAOS APPEARING IN A PERIODICALLY CONTROLLED CSTR , 1984 .

[8]  John L. Hudson,et al.  The dynamics of coupled nonisothermal continuous stirred tank reactors , 1986 .

[9]  J. L. Hudson,et al.  Experiments on low-amplitude forcing of a chemical oscillator , 1986 .

[10]  L. Glass,et al.  Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. , 1981, Science.

[11]  Rutherford Aris,et al.  On the dynamics of periodically forced chemical reactors , 1984 .

[12]  H. Swinney,et al.  Topology of Chaos in a Chemical Reaction , 1981 .

[13]  L Glass,et al.  Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias , 1982, Journal of mathematical biology.

[14]  T. W. Taylor,et al.  Periodic Perturbation of Limit Cycles in an Isothermal CSTR , 1985 .

[15]  Hiroyuki Nagashima,et al.  Experiment on Chaotic Responses of a Forced Belousov-Zhabotinsky Reaction , 1982 .

[16]  J. L. Hudson,et al.  EXPERIMENTAL EVIDENCE OF MULTIPLE OSCILLATORY STATES IN A CONTINUOUS REACTOR , 1985 .

[17]  F. W. Schneider,et al.  Periodic Perturbation of the BZ-Reaction in a CSTR: Chemical Resonance, Entrainment and Quasi-Periodic Behavior , 1985 .

[18]  J. M. Douglas,et al.  Unsteady state process operation , 1966 .

[19]  J. E. Littlewood,et al.  On Non‐Linear Differential Equations of the Second Order: I. the Equation y¨ − k(1‐y2)y˙ + y = bλk cos(λl + α), k Large , 1945 .

[20]  M. Dolnik,et al.  Experimental observations of periodic and chaotic regimes in a forced chemical oscillator , 1984 .