Review Lecture - Instabilities and oscillations in chemical reactions in closed and open systems

This lecture is chiefly concerned with isothermal oscillations in homogeneous systems, and with finding and validating self-consistent models. Emphasis is laid on satisfying basic physical principles and on preserving chemical reasonableness in as simple a manner as possible. The goal is to devise a scheme that can be applied to a wide variety of circumstances to predict new behaviour as well as to interpret what is known, and to form a foundation for later developments and elaborations. This core of the scheme, called the autocatalator, combines an autocatalytic step $A + 2B\rightarrow 3B, rate = k_1 ab^2,$ with catalyst decay $B\rightarrow C, rate = k_2 b.$ These core reactions may display reversibility and they may be accompanied by uncatalysed conversion $A\rightarrow B, \text{rate}=k_u a.$ Particular stress is given to the problem of closed systems. In closed systems, oscillations cannot be indefinitely sustained. In former days it was customary to ignore this inconvenience (and to repeal the law of conservation of matter); today a less unsatisfactory account is possible.