Adaptive synchronization and anticipatory dynamical systems

Abstract

Many biological systems can sense periodical variations in a stimulus input and produce welltimed, anticipatory responses after the input is removed. Such systems show memory effects for retaining timing information in the stimulus and cannot be understood from traditional synchronization consideration of passive oscillatory systems. To understand this anticipatory phenomena, we consider oscillators built from excitable systems with the addition of an adaptive dynamics. With such systems, well-timed post-stimulus responses similar to those from experiments can be obtained. Furthermore, a well-known model of working memory is shown to possess similar anticipatory dynamics when the adaptive mechanism is identified with synaptic facilitation. The last finding suggests that this type of oscillators can be common in neuronal systems with plasticity.PACS numbers: 05.45. Xt, 87.19.lm, 87.19.lv The interaction between a dynamical system capable of oscillatory behavior and an external periodic stimulus input represents the fundamental physics underlying many biological and engineering systems [1,2]. Under the titles of synchronization or entrainment, active studies have been devoted to various aspects of these systems, for example, the existence and degree of synchrony under different parameter conditions, the stability of the synchronous state, the influence of noise [1], and, recently, the efficiency of entrainment [3]. While these mostly involve how the systems enter or stay under the rhythmic interaction, the post-interaction behavior of the systems often plays important roles in many biological functions [4]. This potentially allows the biological systems to recognize the temporal patterns in the environment and produce anticipatory responses to help their survival. Examples of such transient responses following the end of stimulus have been observed in ganglion cells of retina under light stimulus [5], growth of slime mold influenced by varying humidity [6], and the optic tectum of zebrafish conditioned with moving periodic scenery [7]. However, the underlying physics for this time perception mechanism is still unclear and there is a ongoing debate on whether a clock is needed [8].To explain the anticipative dynamics, it has been proposed that the periods of various lengths can be built into the structure of a network with loops of various sizes [9]. External stimulations of a particular period will then activate a particular circuit in the system to provide the memory effect. This implementation of "memory" with pre-fabricated structure is similar in spirit to the phase model used to understand the anticipation of slime mold [6]. In this phase model, oscillators with various periods must be first put into the system before an external stimulation of a particular frequency can be used to entrain or synchronize the oscillators with the same frequency to provide the anticipation effect. An obvious objection to this type of models of pre-fabricated structures is that a continuous change in external periods will not...

Measurement of Anticipative Power of a Retina by Predictive Information

“…It is well known that neural field models for a retina can successfully produce the anticipative tracking of a moving object spatially. It is still not known how a retina can do the same in the time domain [13].…”