Dissipation, Noise and Adaptive Systems

Most dynamical systems are not isolated, but interacting with an embedding environment that may add stochastic components to the evolution equations. The internal dynamics slows down when energy is dissipated to the outside world, approaching attracting states which may be regular, such as fixpoints or limit cycle, or irregular, such as chaotic attractors. Adaptive systems alternate between phases of energy dissipation and uptake, until a balance between these two opposing processes is achieved. In this chapter an introduction to adaptive, dissipative and stochastic systems will be given together with important examples from the realm of noise controlled dynamics, like diffusion, random walks and stochastic escape and resonance. We will discuss to which extent chaos, a regular guest of adaptive systems, may remain predictable.