Noise effects in a dynamic model of attentional switching

Attention plays a crucial role in higher cognition in the presence of limited resources. We study attentional mechanisms producing sequential switching between interacting mental modalities. Our model uses dissipative dynamical systems of coupled oscillators modeling various parts of the brain. The dynamics can manifest winnerless competition (WLC) between the oscillators with switching between different modalities. Heteroclinic cycle is a widely used mathematical image of dynamical switching in WLC. We use the generalized Lotka-Volterra (LV) equations to describe networks with WLC. For simplicity, we assume that there are two subsystems, each is described by three LV equations. Under certain value of mutual coupling one part of the system has topologically equivalent behavior to its initial however the other part exhibits chaotic dynamics. We study the dynamics of the system with intrinsic additive and multiplicative noise components. The coupled attentional system exhibits robust behavior with heteroclinic cycles in the case of multiplicative noise. Additive noise, on the other hand, may lead to the collapse of the complex chaotic dynamics to periodic oscillations.