Some Limit Cycle Oscillations in Nonlinear Kinetic Equations

Some Limit Cycle Oscillations in Nonlinear Kinetic Equations 

Here we consider the problem of determining whether or not there are limit cycle oscillations in kinetic equations with more than two interacting chemicals. To keep definite, we discuss the dynamics of Eq. (27), N = 3, in Sections 4.1 and 4.2, and Eq. (22) in Section 4.3. 

In 1942 Hopf demonstrated a way to establish the presence of oscillations in limited regions of parameter space.The methods developed by Hopf have recently had many applications to study of oscillations in chemical and biological systems. After stating the theorem in general form, I will show how it can be applied to the equation for feedback inhibition. Let us assume that the dynamical system in Eq. (1) depends on the parameter a, so that 

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