19,196 research outputs found
Almost periodic solutions of retarded SICNNs with functional response on piecewise constant argument
We consider a new model for shunting inhibitory cellular neural networks,
retarded functional differential equations with piecewise constant argument.
The existence and exponential stability of almost periodic solutions are
investigated. An illustrative example is provided.Comment: 24 pages, 1 figur
Robust synchronization of an array of coupled stochastic discrete-time delayed neural networks
Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete-time neural networks with time-varying delay. The individual neural network is subject to parameter uncertainty, stochastic disturbance, and time-varying delay, where the norm-bounded parameter uncertainties exist in both the state and weight matrices, the stochastic disturbance is in the form of a scalar Wiener process, and the time delay enters into the activation function. For the array of coupled neural networks, the constant coupling and delayed coupling are simultaneously considered. We aim to establish easy-to-verify conditions under which the addressed neural networks are synchronized. By using the Kronecker product as an effective tool, a linear matrix inequality (LMI) approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally, robustly, exponentially synchronized in the mean square. The LMI-based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time-varying delay, and can be solved efficiently via the Matlab LMI Toolbox. Two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme
Self-organization of network dynamics into local quantized states
Self-organization and pattern formation in network-organized systems emerges
from the collective activation and interaction of many interconnected units. A
striking feature of these non-equilibrium structures is that they are often
localized and robust: only a small subset of the nodes, or cell assembly, is
activated. Understanding the role of cell assemblies as basic functional units
in neural networks and socio-technical systems emerges as a fundamental
challenge in network theory. A key open question is how these elementary
building blocks emerge, and how they operate, linking structure and function in
complex networks. Here we show that a network analogue of the Swift-Hohenberg
continuum model---a minimal-ingredients model of nodal activation and
interaction within a complex network---is able to produce a complex suite of
localized patterns. Hence, the spontaneous formation of robust operational cell
assemblies in complex networks can be explained as the result of
self-organization, even in the absence of synaptic reinforcements. Our results
show that these self-organized, local structures can provide robust functional
units to understand natural and socio-technical network-organized processes.Comment: 11 pages, 4 figure
Bistability: Requirements on Cell-Volume, Protein Diffusion, and Thermodynamics
Bistability is considered wide-spread among bacteria and eukaryotic cells,
useful e.g. for enzyme induction, bet hedging, and epigenetic switching.
However, this phenomenon has mostly been described with deterministic dynamic
or well-mixed stochastic models. Here, we map known biological bistable systems
onto the well-characterized biochemical Schloegl model, using analytical
calculations and stochastic spatio-temporal simulations. In addition to network
architecture and strong thermodynamic driving away from equilibrium, we show
that bistability requires fine-tuning towards small cell volumes (or
compartments) and fast protein diffusion (well mixing). Bistability is thus
fragile and hence may be restricted to small bacteria and eukaryotic nuclei,
with switching triggered by volume changes during the cell cycle. For large
volumes, single cells generally loose their ability for bistable switching and
instead undergo a first-order phase transition.Comment: 23 pages, 8 figure
Towards generalized measures grasping CA dynamics
In this paper we conceive Lyapunov exponents, measuring the rate of separation between two initially close configurations, and Jacobians, expressing the sensitivity of a CA's transition function to its inputs, for cellular automata (CA) based upon irregular tessellations of the n-dimensional Euclidean space. Further, we establish a relationship between both that enables us to derive a mean-field approximation of the upper bound of an irregular CA's maximum Lyapunov exponent. The soundness and usability of these measures is illustrated for a family of 2-state irregular totalistic CA
Stochastic Synchronization of Genetic Oscillator Networks
The study of synchronization among genetic oscillators is essential for the
understanding of the rhythmic phenomena of living organisms at both molecular
and cellular levels. Genetic networks are intrinsically noisy due to natural
random intra- and inter-cellular fluctuations. Therefore, it is important to
study the effects of noise perturbation on the synchronous dynamics of genetic
oscillators. From the synthetic biology viewpoint, it is also important to
implement biological systems that minimizing the negative influence of the
perturbations. In this paper, based on systems biology approach, we provide a
general theoretical result on the synchronization of genetic oscillators with
stochastic perturbations. By exploiting the specific properties of many genetic
oscillator models, we provide an easy-verified sufficient condition for the
stochastic synchronization of coupled genetic oscillators, based on the Lur'e
system approach in control theory. A design principle for minimizing the
influence of noise is also presented. To demonstrate the effectiveness of our
theoretical results, a population of coupled repressillators is adopted as a
numerical example. In summary, we present an efficient theoretical method for
analyzing the synchronization of genetic oscillator networks, which is helpful
for understanding and testing the synchronization phenomena in biological
organisms. Besides, the results are actually applicable to general oscillator
networks.Comment: 14 pages, 4 figure
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