Nonlinear chemical dynamics feedback

One feature that often characterizes systems of interest in nonlinear chemical dynamics is feedback, the influence of a species on the rate of its own production. 

The nonlinearity of chemical processes received considerable attention in the chemical engineering literature. A large number of articles deal with stand-alone chemical reactors, as for example continuously stirred tank reactor (CSTR), tubular reactor with axial dispersion, and packed-bed reactor. The steady state and dynamic behaviour of these systems includes state multiplicity, isolated solutions, instability, sustained oscillations, and exotic phenomena as strange attractors and chaos. In all cases, the main source of nonlinearity is the positive feedback due to the recycle of heat, coupled with the dependence of the reaction rate versus temperature. 

Feedforward control is probably used more in chemical engineering systems than in any other field of engineering. Our systems are often slow-moving, nonlinear, and multivariable, and contain appreciable deadtime. All these characteristics make life miserable for feedback controllers. Feedforward controllers can handle all these with relative ease as long as the disturbances can be measured and the dynamics of the process are known. 

Under non-equilibrium conditions, some nonlinear phenomena such as oscillation, chaos and stationary pattern occur are a result of the loss of stability by the steady states, caused by the feedback loops in the processes determining the dynamics of such systems. Such self-organization can be obvious itself as a function of either only time coordinate including simultaneous oscillations of the entire system s state or only spatial coordinate including Turing stmctures or both coordinates including both traveling and chemical waves. The universal fact discovered of such phenomenon in different systems is remarkable in the context of mathematical description. 

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