Limit-cycle behaviour in a model chemical reaction: the cubic autocatalator

✍ Scribed by L. K. Forbes; C. A. Holmes

• Book ID: 104633749
• Publisher: Springer
• Year: 1990
• Tongue: English
• Weight: 512 KB
• Volume: 24
• Category: Article
• ISSN: 0022-0833
• DOI: 10.1007/bf00129873

✦ Synopsis

Limit cycles are sought in a mathematical model of a simple hypothetical chemical reaction involving essentially only two reacting species. Physically, these limit cycles correspond to time-periodic oscillations in the concentrations of the two chemicals. A combination of analytical and numerical methods reveals that limit-cycle behaviour is only possible in a restricted region of the parameter space. Strong numerical evidence is presented to assert that the limit cycle is unique and stable to infinitesimal perturbations. Numerical solutions are displayed and discussed.