From Chaos to Antichaos and Back to Chaos: The Possibility of a Cyele

Abstract

Chaotic dynamics has become an important field in economics and in many other areas. It is known that a complex non-linear system can generate disorder, and ultimately end up in a state of deterministic chaos. A new development is now the possibility of antichaos. Out of a chaos may suddenly arise a high state of order. Involved is a kind of spontaneous crystallization. In this paper it is shown how in chaos dynamics the sensitive dependence on initial conditions can explain a transition from chaos to antichaos. A small parametric disturbance in the initial conditions suffices to cause such a switch. Yet, the disturbance must be neither too small, nor too large. It must have a sufficient leverage effect and it must come at the right time. One may speculate that imbedded in the structure of deterministic chaos are elements of order and determinateness. These are seemingly dormant, until appropriate disturbances, with implicit steering characteristics, occur. It is possible that a specific sequence of time-dependent disturbances generates a cycle which moves from chaos to antichaos and back to chaos.