4,841 research outputs found
Exponential Lag Synchronization of Cohen-Grossberg Neural Networks with Discrete and Distributed Delays on Time Scales
In this article, we investigate exponential lag synchronization results for
the Cohen-Grossberg neural networks (C-GNNs) with discrete and distributed
delays on an arbitrary time domain by applying feedback control. We formulate
the problem by using the time scales theory so that the results can be applied
to any uniform or non-uniform time domains. Also, we provide a comparison of
results that shows that obtained results are unified and generalize the
existing results. Mainly, we use the unified matrix-measure theory and Halanay
inequality to establish these results. In the last section, we provide two
simulated examples for different time domains to show the effectiveness and
generality of the obtained analytical results.Comment: 20 pages, 18 figure
Integration of continuous-time dynamics in a spiking neural network simulator
Contemporary modeling approaches to the dynamics of neural networks consider
two main classes of models: biologically grounded spiking neurons and
functionally inspired rate-based units. The unified simulation framework
presented here supports the combination of the two for multi-scale modeling
approaches, the quantitative validation of mean-field approaches by spiking
network simulations, and an increase in reliability by usage of the same
simulation code and the same network model specifications for both model
classes. While most efficient spiking simulations rely on the communication of
discrete events, rate models require time-continuous interactions between
neurons. Exploiting the conceptual similarity to the inclusion of gap junctions
in spiking network simulations, we arrive at a reference implementation of
instantaneous and delayed interactions between rate-based models in a spiking
network simulator. The separation of rate dynamics from the general connection
and communication infrastructure ensures flexibility of the framework. We
further demonstrate the broad applicability of the framework by considering
various examples from the literature ranging from random networks to neural
field models. The study provides the prerequisite for interactions between
rate-based and spiking models in a joint simulation
Anti-periodic solution for fuzzy Cohen–Grossberg neural networks with time-varying and distributed delays
In this paper, by using a continuation theorem of coincidence degree theory and a differential inequality, we establish some sufficient conditions ensuring the existence and global exponential stability of anti-periodic solutions for a class of fuzzy Cohen–Grossberg neural networks with time-varying and distributed delays. In addition, we present an illustrative example to show the feasibility of obtained results
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