In chemistry and in chemical engineering there is a tacit doctrine that homogeneous isothermal reactors, even ones with highly complex chemistry, behave in very stable ways, regardless of parameter values. Although this doctrine is supported in large part by a long and rich observational record, there are certainly instances of isothermal reactors that give rise, for example, to multiple steady states. Indeed, evolution would seem to favor biological systems that can switch between two very different steady states in response to external signals. It would appear, then, that, across the great and varied landscape of complex reaction networks, there are large expanses having a kind of built-in stability but also smaller regions in which (perhaps biologically purposeful) instabilities are extant.

As early as 1955, Neal Amundson recognized that the stability of complex isothermal reactors should not be taken for granted but, instead, questioned and studied. More than a half century later, we are beginning to understand the big picture in a comprehensive way. I will present some recent work, with Gheorghe Craciun, that suggests why, in homogenous isothermal settings, “most” intricate reaction networks behave stably, regardless of parameter values, and why, on the other hand, even very simple biochemical systems can be prone to instability.