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In the analysis of time series from nonlinear sources, mutual information (MI) is used as a nonlinear statistical criterion for the selection of an appropriate time delay in time delay reconstruction of the state space. MI is a statistic over the sets of sequences associated with the dynamical source, and we examine here the distribution of MI, thus going beyond the familiar analysis of its average alone. We give for the first time the distribution of MI for a standard, classical communications channel with Gaussian, additive white noise. For time series analysis of a dynamical system, we show how to determine the distribution of MI and discuss the implications for the use of average mutual information (AMI) in selecting time delays in phase space reconstruction., Comment: 4 pages, 2 figures, RevTeX V4b4, submitted to Phys. Rev. Lett

We report on experimental studies of synchronization phenomena in a pair of analog electronic neurons (ENs). The ENs were designed to reproduce the observed membrane voltage oscillations of isolated biological neurons from the stomatogastric ganglion of the California spiny lobster Panulirus interruptus. The ENs are simple analog circuits which integrate four dimensional differential equations representing fast and slow subcellular mechanisms that produce the characteristic regular/chaotic spiking-bursting behavior of these cells. In this paper we study their dynamical behavior as we couple them in the same configurations as we have done for their counterpart biological neurons. The interconnections we use for these neural oscillators are both direct electrical connections and excitatory and inhibitory chemical connections: each realized by analog circuitry and suggested by biological examples. We provide here quantitative evidence that the ENs and the biological neurons behave similarly when coupled in the same manner. They each display well defined bifurcations in their mutual synchronization and regularization. We report briefly on an experiment on coupled biological neurons and four dimensional ENs which provides further ground for testing the validity of our numerical and electronic models of individual neural behavior. Our experiments as a whole present interesting new examples of regularization and synchronization in coupled nonlinear oscillators., Comment: 26 pages, 10 figures

Central Pattern Generators (CPGs) in invertebrates are comprised of networks of neurons in which every neuron has reciprocal connections to other members of the CPG. This is a ``closed'' network topology. An ``open'' topology, where one or more neurons receives input but does not send output to other member neurons, is not found in these CPGs. In this paper we investigate a possible reason for this topological structure using the ability to perform a biological functional task as a measure of the efficacy of the network. When the CPG is composed of model neurons which exhibit regular membrane voltage oscillations, open topologies are essentially as able to maximize this functionality as closed topologies. When we replace these models by neurons which exhibit chaotic membrane voltage oscillations, the functional criterion selects closed topologies when the demands of the task are increased, and these are the topologies observed in known CPG networks. As isolated neurons from invertebrate CPGs are known in some cases to undergo chaotic oscillations (Abarbanel et al 1996, Hayashi Ishuzuka 1992) this provides a biological basis for understanding the class of closed network topologies we observe., Comment: 16 pages, 6 figures

Studies of insect olfactory processing indicate that odors are represented by rich spatio-temporal patterns of neural activity. These patterns are very difficult to predict a priori, yet they are stimulus specific and reliable upon repeated stimulation with the same input. We formulate here a theoretical framework in which we can interpret these experimental results. We propose a paradigm of ``dynamic competition'' in which inputs (odors) are represented by internally competing neural assemblies. Each pattern is the result of dynamical motion within the network and does not involve a ``winner'' among competing possibilities. The model produces spatio-temporal patterns with strong resemblance to those observed experimentally and possesses many of the general features one desires for pattern classifiers: large information capacity, reliability, specific responses to specific inputs, and reduced sensitivity to initial conditions or influence of noise. This form of neural processing may thus describe the organizational principles of neural information processing in sensory systems and go well beyond the observations on insect olfactory processing which motivated its development., Comment: 19 pages, 16 figures. Originally submitted to the neuro-sys archive which was never publicly announced (was 9905002)