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Retrieval of episodic memory is a dynamical process in the large scale brain networks. In social groups, the neural patterns, associated to specific events directly experienced by single members, are encoded, recalled and shared by all participants. Here we construct and study the dynamical model for the formation and maintaining of episodic memory in small ensembles of interacting brains. We prove that the unconventional dynamical attractor of this process - the nonsmooth heteroclinic torus - is structurally stable within the Lotka-Volterra-like sets of equations. Dynamics on this torus combines absence of chaos with asymptotic instability of every separate trajectory; its adequate quantitative characteristics are length-related Lyapunov exponents. Variation of the coupling strength between the participants results in different types of sequential switching between metastable states; we interpret them as stages in formation and modification of the episodic memory., Comment: 16 pages, 14 figures

We present a new paradigm in the study of brain mental dynamics on the basis of the stable transient activity neural networks observed in experiments. This new approach is in contrast to traditional system analysis usually adopted in cognitive modeling. Transient dynamics offers a sound formalism of the observed qualities of brain activity, while providing a rigorous set of analysis tools. Transients have two main features: First, they are resistant to noise, and reliable even in the face of small variations in initial conditions; the sequence of states visited by the system (its trajectory), is thus structurally stable. Second, the transients are input-specific, and thus convey information about what caused them in the first place. This new dynamical view manifests a rigorous explanation of how perception, cognition, emotion, and other mental processes evolve as a sequence of activity patterns in the brain, and, most importantly, how they interfere with each other. The ideas discussed and demonstrated here lead to the creation of a quantitative theory of the human mental activity and can be deployed on artificial agents.

The ability of nonlinear dynamical systems to process incoming information is a key problem of many fundamental and applied sciences. Information processing by computation with attractors (steady states, limit cycles and strange attractors) has been a subject of many publications. In this paper we discuss a new direction in information dynamics based on neurophysiological experiments that can be applied for the explanation and prediction of many phenomena in living biological systems and for the design of new paradigms in neural computation. This new concept is the Winnerless Competition (WLC) principle. The main point of this principle is the transformation of the incoming identity or spatial inputs into identity-temporal output based on the intrinsic switching dynamics of the neural system. In the presence of stimuli the sequence of the switching, whose geometrical image in the phase space is a heteroclinic contour, uniquely depends on the incoming information. The key problem in the realization of the WLC principle is the robustness against noise and, simultaneously, the sensitivity of the switching to the incoming input. In this paper we prove two theorems about the stability of the sequential switching and give several examples of WLC networks that illustrate the coexistence of sensitivity and robustness., Comment: 31 pages, 8 figures, in press for International Journal of Bifurcation and Chaos (2004) Vol. 14 (4)

We study the synchronization of two model neurons coupled through a synapse having an activity-dependent strength. Our synapse follows the rules of Spike-Timing Dependent Plasticity (STDP). We show that this plasticity of the coupling between neurons produces enlarged frequency locking zones and results in synchronization that is more rapid and much more robust against noise than classical synchronization arising from connections with constant strength. We also present a simple discrete map model that demonstrates the generality of the phenomenon., Comment: 4 pages, accepted for publication in PRE

We introduce a new biologically-motivated model of sequential spatial memory which is based on the principle of winnerless competition (WLC). We implement this mechanism in a two-layer neural network structure and present the learning dynamics which leads to the formation of a WLC network. After learning, the system is capable of associative retrieval of pre-recorded sequences of spatial patterns., Comment: 4 pages, submitted to PRL

We report experimental studies of synchronization phenomena in a pair of biological neurons that interact through naturally occurring, electrical coupling. When these neurons generate irregular bursts of spikes, the natural coupling synchronizes slow oscillations of membrane potential, but not the fast spikes. By adding artificial electrical coupling we studied transitions between synchrony and asynchrony in both slow oscillations and fast spikes. We discuss the dynamics of bursting and synchronization in living neurons with distributed functional morphology., Comment: 4 pages, 6 figures, to be published in PRL