Onset of Phase Synchronization in Neurons Conneted via Chemical Synapses

We study the onset of synchronous states in realistic chaotic neurons coupled by mutually inhibitory chemical synapses. For the realistic parameters, namely the synaptic strength and the intrinsic current, this synapse introduces non-coherences in the neuronal dynamics, yet allowing for chaotic phase synchronization in a large range of parameters. As we increase the synaptic strength, the neurons undergo to a periodic state, and no chaotic complete synchronization is found.Comment: to appear in Int. J. Bif. Chao

Transient spatiotemporal chaos in a diffusively and synaptically coupled Morris-Lecar neuronal network

Thesis (M.S.) University of Alaska Fairbanks, 2014Transient spatiotemporal chaos was reported in models for chemical reactions and in experiments for turbulence in shear flow. This study shows that transient spatiotemporal chaos also exists in a diffusively coupled Morris-Lecar (ML) neuronal network, with a collapse to either a global rest state or to a state of pulse propagation. Adding synaptic coupling to this network reduces the average lifetime of spatiotemporal chaos for small to intermediate coupling strengths and almost all numbers of synapses. For large coupling strengths, close to the threshold of excitation, the average lifetime increases beyond the value for only diffusive coupling, and the collapse to the rest state dominates over the collapse to a traveling pulse state. The regime of spatiotemporal chaos is characterized by a slightly increasing Lyapunov exponent and degree of phase coherence as the number of synaptic links increases. In contrast to the diffusive network, the pulse solution must not be asymptotic in the presence of synapses. The fact that chaos could be transient in higher dimensional systems, such as the one being explored in this study, point to its presence in every day life. Transient spatiotemporal chaos in a network of coupled neurons and the associated chaotic saddle provide a possibility for switching between metastable states observed in information processing and brain function. Such transient dynamics have been observed experimentally by Mazor, when stimulating projection neurons in the locust antennal lobe with different odors

The Utility of Phase Models in Studying Neural Synchronization

Synchronized neural spiking is associated with many cognitive functions and thus, merits study for its own sake. The analysis of neural synchronization naturally leads to the study of repetitive spiking and consequently to the analysis of coupled neural oscillators. Coupled oscillator theory thus informs the synchronization of spiking neuronal networks. A crucial aspect of coupled oscillator theory is the phase response curve (PRC), which describes the impact of a perturbation to the phase of an oscillator. In neural terms, the perturbation represents an incoming synaptic potential which may either advance or retard the timing of the next spike. The phase response curves and the form of coupling between reciprocally coupled oscillators defines the phase interaction function, which in turn predicts the synchronization outcome (in-phase versus anti-phase) and the rate of convergence. We review the two classes of PRC and demonstrate the utility of the phase model in predicting synchronization in reciprocally coupled neural models. In addition, we compare the rate of convergence for all combinations of reciprocally coupled Class I and Class II oscillators. These findings predict the general synchronization outcomes of broad classes of neurons under both inhibitory and excitatory reciprocal coupling.Comment: 18 pages, 5 figure

General Framework for phase synchronization through localized sets

We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another one whenever this event occurs, these observations give rise to a localized set. Our result provides a general and easy way to identify PS, which can also be used to oscillators that possess multiple time scales. We illustrate our approach in networks of chemically coupled neurons. We show that clusters of phase synchronous neurons may emerge before the onset of phase synchronization in the whole network, producing a suitable environment for information exchanging. Furthermore, we show the relation between the localized sets and the amount of information that coupled chaotic oscillator can exchange

Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA