Transient cognitive dynamics, metastability, and decision making

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.

Figure 1. Schematic representation of a stable heteroclinic channel.

The SHC is built with trajectories that condense in the vicinity of the saddle chain and their unstable separatrices (dashed lines) connecting the surrounding saddles (circles). The thick line represents an example of a trajectory in the SHC. The interval t_{k +1}−t_k is the characteristic time that the system needs to move from the metastable state k to the k+1.

Figure 2. Closed stable heteroclinic sequence in the phase space of three coupled clusters.

(A) Wilson-Cowan clusters. (B) Lotka-Volterra clusters.

Figure 3. Robust transient dynamics of 200 cognitive modes modeled with Wilson-Cowan equations.

(A) The activation level of three cognitive modes are shown (E14, E11, E35), (B) Time series illustrating sequential switching between modes: 10 different modes out of the total 200 interacting modes are shown.

Figure 4. Reproducibility of a transient sequential dynamics of 20 metastable modes corresponding to SHC in Model 4.

The figure shows the time series of 10 trials. Simulations of each trial were initiated at a different random initial condition. The initial conditions influence the trajectory only at the beginning due to the dissipativeness of the saddles (for details see also [10]).

Figure 5. Estimation of the cumulative reward for different noise levels using multiplicative noise.

(A) Cumulative reward calculated as the number of cognitive states that the system travels through until the final time of the game T* which is 100 in this case. For each level of noise, 1000 different sequences are generated (for N = 15 and a total of 15 choices). (B) Reproducibility index of the sequence calculated with the average Levenshtein distance across all generated sequences. The lower the distance, the more similar the sequences are for 1000 different runs. The pair distances are calculated and averaged to obtain the mean and the standard deviation which is represented by the error bars.