A computational tool for nonlinear dynamical and bifurcation analysis of chemical engineering problems
We present a program package CONT for modelling and analysis of nonlinear problems and use it to solve chemical engineering problems including chemical reactors and adsorption columns. Model should be in the form of ordinary differential equations (ODEs), spatially distributed systems described by partial differential equations may also be treated upon transformation to ODEs by a built-in discretization. Continuation of a steady state, periodic solution or solution of a general boundary value problem with respect to a parameter provides a solution diagram; simultaneous stability analysis identifies bifurcation points and these may be continued with respect to a second parameter to obtain a bifurcation diagram. Additionally, the program performs a direct integration of ODEs, calculates Poincare orbits and Lyapunov exponents, and possesses other functionalities useful for practical analysis of complex dynamics. Three example problems are analyzed and discussed in detail: (1) dynamical and bifurcation patterns in a stirred reactor and a tubular reactor with a metabolic biochemical reaction; (2) shock waves in an adsorption column; (3) pulse waves in a model of intracellular calcium dynamics. (C) 2002 Elsevier Science Ltd. All rights reserved.
bifurcation continuation reaction-diffusion system chemical waves dynamical systems