Learning-induced synchronization of a globally coupled excitable map system

Pipe flow of magneto-micropolar fluids with slip

The steady unidirectional flow of an isothermal, incompressible, magneto-micropolar hydrodynamic fluid in an infinitely magnetic insulating circular cylinder is considered. The fluid is under a constant magnetic field perpendicular to the axis of the cylinder. The slip boundary conditions for velocity and microrotation are applied. Closed forms for the velocity, microrotation, and magnetic field are obtained for Poiseuille and Couette flows. Expressions for the rate of flow and skin coefficients are calculated. Variations of the physical quantities with respect to micropolarity parameter, slip parameters, and Hartman number are studied and their variations are illustrated graphically. Similar results are obtained for electro- micropolar fluids.

Growth of cortical neuronal network in vitro: modeling and analysis

We present a detailed analysis and theoretical growth models to account for recent experimental data on the growth of cortical neuronal networks in vitro [Phys. Rev. Lett. 93, 088101 (2004)]. The experimentally observed synchronized firing frequency of a well-connected neuronal network is shown to be proportional to the mean network connectivity. The growth of the network is consistent with the model of an early enhanced growth of connection, but followed by a retarded growth once the synchronized cluster is formed. Microscopic models with dominant excluded volume interactions are consistent with the observed exponential decay of the mean connection probability as a function of the mean network connectivity. The biological implications of the growth model are also discussed.

Learning-Induced Synchronization and Plasticity of a Developing Neural Network

Learning-induced synchronization of a neural network at various developing stages is studied by computer simulations using a pulse-coupled neural network model in which the neuronal activity is simulated by a one-dimensional map. Two types of Hebbian plasticity rules are investigated and their differences are compared. For both models, our simulations show a logarithmic increase in the synchronous firing frequency of the network with the culturing time of the neural network. This result is consistent with recent experimental observations. To investigate how to control the synchronization behavior of a neural network after learning, we compare the occurrence of synchronization for four networks with different designed patterns under the influence of an external signal. The effect of such a signal on the network activity highly depends on the number of connections between neurons. We discuss the synaptic plasticity and enhancement effects for a random network after learning at various developing stages.

Connectivities and synchronous firing in cortical neuronal networks

Network connectivities ((-)k) of cortical neural cultures are studied by synchronized firing and determined from measured correlations between fluorescence intensities of firing neurons. The bursting frequency (f) during synchronized firing of the networks is found to be an increasing function of (-)k. With f taken to be proportional to (-)k, a simple random model with a (-)k dependent connection probability p((-)k).has been constructed to explain our experimental findings successfully.

Noise-induced macroscopic bifurcations in globally coupled chaotic units

Large populations of globally coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that, for strong coupling, the collective dynamics can be described in terms of a few effective macroscopic degrees of freedom, whose deterministic equations of motion are systematically derived through an order parameter expansion.

Delayed coupling of logistic maps

We study the synchronization of logistic maps in a one-way coupling configuration. The master system is coupled to the slave system with a delay n(1), and the slave is a delayed logistic map with a delay n(2). We show that when the slave system has no delay (n(2)=0), perfectly synchronized solutions exist for strong enough coupling. In these solutions the slave variable y is retarded with respect to the master variable x with a retardation equal to the delay of the coupling [y(i+n(1))=x(i)]. When n(2) not equal 0, a regime of generalized synchronization is observed, where y(i+n(1)) is synchronized with x(i), but not completely, since the master and the slave systems obey different maps. We introduced a similarity function as an indicator of the degree of synchronization and, using a noisy master source, distinguished synchronization from noise-induced correlations.