Some Models with Scalar Equations

It is important to introduce the reader at an early stage to simple examples of nonlinear models. We will first present cases with bifurcation behavior as the more general case, followed by special cases without bifurcation. Note that this is deliberately the reverse of the opposite and more common approach. We take this path because it sets the important precedent of studying chemical and biological engineering systems first in light of their much more prevalent multiple steady states rather than from the rarer occurrence of a unique steady state. 

One of the simplest practical examples is the homogeneous nonisothermal and adiabatic continuous stirred tank reactor (CSTR), whose steady state is described by nonlinear transcendental equations and whose unsteady state is described by nonlinear ordinary differential equations. 

We will consider a very simple irreversible reaction 

Chapter 3 Some Models with Scalar Equations 

Under the simple assumptions of constant volume V and volumetric flow rate q, the steady states of the system are described by the two equations 

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