Modular Neurodynamics and Its Classification by Synchronization Cores

Abstract

It is assumed that the cause of cognitive and behavioral capacities of living systems is to be found in the complex structure-function relationship of their brains; a property that is still difficult to decipher. Based on a neurodynamics approach to embodied cognition this paper introduces a method to guide the development of modular neural systems into the direction of enhanced cognitive abilities. It uses formally the synchronization of subnetworks to split the dynamics of coupled systems into synchronized and asynchronous components. The concept of a synchronization core is introduced to represent a whole family of parameterized neurodynamical systems living in a synchronization manifold. It is used to identify those coupled systems having a rich spectrum of dynamical properties. Special coupling structures—called generative—are identified which allow to make the synchronized dynamics more “complex” than the dynamics of the isolated parts. Furthermore, a criterion for coupling structures is given which, in addition to the synchronized dynamics, allows also for an asynchronous dynamics by destabilizing the synchronization manifold. The large class of synchronization equivalent systems contains networks with very different coupling structures and weights allsharing the same dynamical properties. To demonstrate the method a simple example is discussed in detail.