Towards Analytical Chaotic Evolutions in Brusselators

The Brusselator is a mathematical model for autocatalytic reaction, which was proposed by Ilya Prigogine and his collaborators at the Universit Libre de Bruxelles. The dynamics of the Brusselator gives an oscillating reaction mechanism for an autocatalytic, oscillating chemical reaction. The Brusselator is a slow-fast oscillating chemical reaction system. The traditional analytical methods cannot provide analytical solutions of such slow-fast oscillating reaction, and numerical simulations cannot provide a full picture of periodic evolutions in the Brusselator. In this book, the generalized harmonic balance methods are employed for analytical solutions of periodic evolutions of the Brusselator with a harmonic diffusion. The bifurcation tree of period-1 motion to chaos of the Brusselator is presented through frequency-amplitude characteristics, which be measured in frequency domains. Two main results presented in this book are:

- analytical routes of periodical evolutions to chaos and

- independent period-(2