About the oscillatory possibilities of the dynamical systems

TL;DR

This paper explores a nonlinear mechanism for oscillatory mode mixing in dynamical systems, proposing a scenario that explains complex behaviors in physical devices, turbulence, and brain activity, and offers a framework for understanding evolutionary complexity.

Contribution

It introduces a novel nonlinear mechanism and a generic dynamical scenario that accounts for complex oscillatory behaviors and evolutionary development in deterministic systems.

Findings

Describes a nonlinear oscillatory mode mixing mechanism.

Establishes a dynamical scenario with scalable oscillatory possibilities.

Links the scenario to turbulence and brain dynamics.

Abstract

This paper attempts to make feasible the evolutionary emergence of novelty in a supposedly deterministic world which behavior is associated with those of the mathematical dynamical systems. The work was motivated by the observation of complex oscillatory behaviors in a family of physical devices, for which there is no known explanation in the mainstream of nonlinear dynamics. The paper begins by describing a nonlinear mechanism of oscillatory mode mixing explaining such behaviors and establishes a generic dynamical scenario with extraordinary oscillatory possibilities, including expansive growing scalability. The relation of the scenario to the oscillatory behaviors of turbulent fluids and living brains is discussed. Finally, by considering the scenario as a dynamic substrate underlying generic aspects of both the functioning and the genesis of complexity in a supposedly deterministic world, a theoretical framework covering the evolutionary development of structural transformations in the time evolution of that world is built up.