Synchronous Behavior of Two Coupled Electronic Neurons

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 figure

Self-synchronization and controlled synchronization

An attempt is made to give a general formalism for synchronization in dynamical systems encompassing most of the known definitions and applications. The proposed set-up describes synchronization of interconnected systems with respect to a set of functionals and captures peculiarities of both self-synchronization and controlled synchronization. Various illustrative examples are give

Complex partial synchronization patterns in networks of delay-coupled neurons

We study the spatio-temporal dynamics of a multiplex network of delay-coupled FitzHugh–Nagumo oscillators with non-local and fractal connectivities. Apart from chimera states, a new regime of coexistence of slow and fast oscillations is found. An analytical explanation for the emergence of such coexisting partial synchronization patterns is given. Furthermore, we propose a control scheme for the number of fast and slow neurons in each layer.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept

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