Abstract
The idea that cognitive activity can be understood using nonlinear dynamics has been intensively discussed at length for the last 15 years. One of the popular points of view is that metastable states play a key role in the execution of cognitive functions. Experimental and modeling studies suggest that most of these functions are the result of transient activity of large-scale brain networks in the presence of noise. Such transients may consist of a sequential switching between different metastable cognitive states. The main problem faced when using dynamical theory to describe transient cognitive processes is the fundamental contradiction between reproducibility and flexibility of transient behavior. In this paper, we propose a theoretical description of transient cognitive dynamics based on the interaction of functionally dependent metastable cognitive states. The mathematical image of such transient activity is a stable heteroclinic channel, i.e., a set of trajectories in the vicinity of a heteroclinic skeleton that consists of saddles and unstable separatrices that connect their surroundings. We suggest a basic mathematical model, a strongly dissipative dynamical system, and formulate the conditions for the robustness and reproducibility of cognitive transients that satisfy the competing requirements for stability and flexibility. Based on this approach, we describe here an effective solution for the problem of sequential decision making, represented as a fixed time game: a player takes sequential actions in a changing noisy environment so as to maximize a cumulative reward. As we predict and verify in computer simulations, noise plays an important role in optimizing the gain.
Highlights
The dynamical approach for studying brain activity has a long history and is currently one of strong interest [1,2,3,4,5,6,7]
Cognitive functions such as sequential learning, shortterm memory, and decision making in a changing environment cannot be understood using only the traditional view based on classical concepts of nonlinear dynamics, which describe static or rhythmic brain activity
We propose a new class of models for the analysis of transient dynamics that can be applied for sequential decision making
Summary
The dynamical approach for studying brain activity has a long history and is currently one of strong interest [1,2,3,4,5,6,7]. The execution of cognitive functions is based on fundamental asymmetries of time – often metaphorically described as the arrow of time. This is inseparably connected to the temporal ordering of cause-effect pairs. The correspondence between causal relations and temporal directions requires specific features in the organization of cognitive system interactions, and on the microscopic level, specific network interconnections. A key requirement for this organization is the presence of nonsymmetrical interactions because, even in brain resting states, the interaction between different subsystems of cognitive modes produces nonstationary activity that has to be reproducible. One plausible mechanism of mode interaction that supports temporal order is nonreciprocal competition. At all levels of network complexity, the physiological mechanisms of competition are mainly implemented through inhibitory connections. As we have shown in [5,10], nonsymmetric inhibition is an origin of reproducible transients in neural networks
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