Nonlinear feedback beyond stability: its role in complex systems

The main purpose of this paper is to call the control engineers' attention to the exciting results with nonlinear feedback beyond the boundary of stability, recently obtained in dealing with complex systems in the nonengineering sciences, and to look upon these results from an engineering point of view. Complex systems containing many interdependent components and nonlinear feedback, the source of their nonlinear dynamics, are currently intensively studied beyond the boundary of stability in the natural sciences, economics, and the social sciences. In this paper the fundamental importance of nonlinear feedback is pointed out and its decisive part in the generation of order, chaos and fractals is demonstrated in terms of a simple example, the logistic equation. Emphasis is then placed upon the strange behaviour of complex systems that operate in the narrow zone between stability and instability, which apparently describes the mechanism of biological systems and their evolution. Some examples of useful application of these results in engineering are given.