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ABSTRACT: How can precise control be realised in intrinsically noisy systems? Here, we
develop a general theoretical framework that provides a way to achieve precise
control in signal-dependent noisy environments. When the control signal has
Poisson or supra-Poisson noise, precise control is not possible. If, however,
the control signal has sub-Poisson noise, then precise control is possible. For
this case, the precise control solution is not a function, but a rapidly
varying random process that must be averaged with respect to a governing
probability density functional. Our theoretical approach is applied to the
control of straight-trajectory arm movement. Sub-Poisson noise in the control
signal is shown to be capable of leading to precise control. Intriguingly, the
control signal for this system has a natural counterpart, namely the bursting
pulses of neurons --trains of Dirac-delta functions-- in biological systems to
achieve precise control performance.
04/2013;
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ABSTRACT: In this paper, we consider cluster synchronization in an uncertain generic neural network. The network is composed of many
interactional clusters, including inner couplings in each cluster and outer couplings between different clusters. For the
neural network, the dynamics of each cluster can be unknown and different. The coupling functions including uniform and nonuniform
couplings between clusters can be unknown, too. By adding some time-varying linear and negative feedback controllers, we can
guarantee that every cluster will synchronize at an arbitrary pre-assigned state/orbit of an isolated cluster of the network.
Numerical simulations are presented to show the validity of the theoretical results.
KeywordsUncertain neural networks–Cluster synchronization–Adaptive controllers
Differential Equations and Dynamical Systems 04/2012; 19(1):47-61.
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ABSTRACT: In this paper, a new approach to analyze synchronization of linearly coupled map lattices (LCMLs) is presented. A reference
vector
$
\ifmmode\expandafter\hat\else\expandafter\^\fi{x}
$
\ifmmode\expandafter\hat\else\expandafter\^\fi{x}
(t) is introduced as the projection of the trajectory of the coupled system on the synchronization manifold. The stability analysis
of the synchronization manifold can be regarded as investigating the difference between the trajectory and the projection.
By this method, some criteria are given for both local and global synchronization. These criteria indicate that the left and
right eigenvectors corresponding to the eigenvalue "0" of the coupling matrix play key roles in the stability of synchronization
manifold for the coupled system. Moreover, it is revealed that the stability of synchronization manifold for the coupled system
is different from the stability for dynamical system in usual sense. That is, the solution of the coupled system does not
converge to a certain knowable s(t) satisfying s(t+1) = f(s(t)) but to the reference vector on the synchronization manifold, which in fact is a certain weighted average of each x
i
(t) for i = 1, ⋯ ,m, but not a solution s(t) satisfying s(t + 1) = f(s(t)).
Chinese Annals of Mathematics 04/2012; 28(2):149-160. · 0.52 Impact Factor
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ABSTRACT: In this paper, we discuss the asymptotic stability of the trajectories governed by the scalar delay differential inequalities: D⁺x(t)≤-a(t)x(t)+b(t)sup(0≤s≤τ)x(t-s). Here, the requirements on a(t) and b(t) are more relaxed than those in previous works. For example, a(t), b(t), and a(t)-b(t) are not necessarily nonnegative. We prove that when τ is small, the asymptotic stability of x(t) can be obtained if the time average of a(t)-b(t) on some fixed length T is lower bounded by some positive δ. And we explicitly give the upper bound of τ. We also give two applications of the theoretical results. First, we consider self synchronization in Hopfield networks with time varying connections. Then we investigate consensus in networks with time varying topologies and arbitrary coupling weights. In both applications, we extend some of our previous works where time delays are not considered. At last, two numerical examples with simulations are provided to illustrate the effectiveness of the theoretical results.
Neural networks: the official journal of the International Neural Network Society 04/2012; 33:1-6. · 1.88 Impact Factor
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ABSTRACT: In this paper, cluster consensus of multi-agent systems is studied via
inter-cluster nonidentical inputs. Here, we consider general graph topologies,
which might be time-varying. The cluster consensus is defined by two aspects:
the intra-cluster synchronization, that the state differences between each pair
of agents in the same cluster converge to zero, and inter-cluster separation,
that the states of the agents in different clusters are separated. For
intra-cluster synchronization, the concepts and theories of consensus including
the spanning trees, scramblingness, infinite stochastic matrix product and
Hajnal inequality, are extended. With them, it is proved that if the graph has
cluster spanning trees and all vertices self-linked, then static linear system
can realize intra-cluster synchronization. For the time-varying coupling cases,
it is proved that if there exists T>0 such that the union graph across any
T-length time interval has cluster spanning trees and all graphs has all
vertices self-linked, then the time-varying linear system can also realize
intra-cluster synchronization. Under the assumption of common inter-cluster
influence, a sort of inter-cluster nonidentical inputs are utilized to realize
inter-cluster separation, that each agent in the same cluster receives the same
inputs and agents in different clusters have different inputs. In addition, the
boundedness of the infinite sum of the inputs can guarantee the boundedness of
the trajectory. As an application, we employ a modified non-Bayesian social
learning model to illustrate the effectiveness of our results.
01/2012;
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IEEE Trans. Automat. Contr. 01/2012; 57:754-760.
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ABSTRACT: Complex neuronal networks are an important tool to help explain paradoxical phenomena observed in biological recordings. Here we present a general approach to mathematically tackle a complex neuronal network so that we can fully understand the underlying mechanisms. Using a previously developed network model of the milk-ejection reflex in oxytocin cells, we show how we can reduce a complex model with many variables and complex network topologies to a tractable model with two variables, while retaining all key qualitative features of the original model. The approach enables us to uncover how emergent synchronous bursting can arise from a neuronal network which embodies known biological features. Surprisingly, the bursting mechanisms are similar to those found in other systems reported in the literature, and illustrate a generic way to exhibit emergent and multiple time scale oscillations at the membrane potential level and the firing rate level.
PLoS ONE 01/2012; 7(6):e38402. · 4.09 Impact Factor
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ABSTRACT: In this paper, we study synchronization of networks of linearly coupled dynamical systems. The node dynamics of the network can be very general, which may not satisfy the QUAD condition. We derive sufficient conditions for synchronization, which can be regarded as extensions of previous results. These results can be employed to networks of coupled systems, of which, in particular, the node dynamics have non-Lipschitz or even discontinuous right-hand sides. We also give several corollaries where the synchronization of some specific non-QUAD systems can be deduced. As an application, we propose a scheme to realize synchronization of coupled switching systems via coupling the signals which drive the switchings. Examples with numerical simulations are also provided to illustrate the theoretical results.
Neural networks: the official journal of the International Neural Network Society 08/2011; 25(1):5-13. · 1.88 Impact Factor
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ABSTRACT: In this paper, global dissipativity and quasi-synchronization issues are investigated for the delayed neural networks with discontinuous activation functions. Under the framework of Filippov solutions, the existence and dissipativity of solutions can be guaranteed by the matrix measure approach and the new obtained generalized Halanay inequalities. Then, for the discontinuous master-response systems with parameter mismatches, quasi-synchronization criteria are obtained by using feedback control. Furthermore, when the proper approximate functions are selected, the complete synchronization can be discussed as a special case that two systems are identical. Numerical simulations on the chaotic systems are presented to demonstrate the effectiveness of the theoretical results.
Neural networks: the official journal of the International Neural Network Society 06/2011; 24(10):1013-21. · 1.88 Impact Factor
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ABSTRACT: In this paper, we discuss Hopfield neural networks with stochastic switching weights, investigating their global almost sure self-synchronization. Sufficient conditions ensuring global almost sure exponential synchronization of Hopfield neural networks with stochastic switching weights are given.
Neural networks: the official journal of the International Neural Network Society 04/2011; 24(3):305-10. · 1.88 Impact Factor
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SIAM J. Control and Optimization. 01/2011; 49:227-253.
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IEEE Transactions on Neural Networks. 01/2011; 22:1508-1513.
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ABSTRACT: In this paper, we study the distribution of attraction basins of multiple equilibrium points of cellular neural networks (CNNs). Under several conditions, the boundaries of the attracting basins of the stable equilibria of a completely stable CNN system are composed of the closures of the stable manifolds of unstable equilibria of (n - 1) dimensions. As demonstrations of this idea, under the conditions proposed in the literature which depicts stable and unstable equilibria, we identify the attraction basin of each stable equilibrium of which the boundary is composed of the stable manifolds of the unstable equilibria precisely. We also investigate the attracting basins of a simple class of symmetric 1-D CNNs via identifying the unstable equilibria of which the stable manifold is (n - 1) dimensional and the completely stable asymmetric CNNs with stable equilibria less than 2(n).
IEEE Transactions on Neural Networks 01/2011; 22(3):381-94. · 2.95 Impact Factor
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Advances in Neural Networks - ISNN 2011 - 8th International Symposium on Neural Networks, ISNN 2011, Guilin, China, May 29-June 1, 2011, Proceedings, Part I; 01/2011
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ABSTRACT: In this note, the consensus problem with infinite time-varying delays for linearly coupled static network is investigated. The delay affects only the off-diagonal terms in continuous-time equations. At first, we define an effective consensus ability index. Then, by using the graph theory and a new concept of consensus, we prove that under some mild conditions, the network can realize consensus. An example is given to show the validity of obtained results.
IEEE Transactions on Automatic Control 11/2010; · 2.11 Impact Factor
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ABSTRACT: Artificial neural networks arise from the research of the configuration and function of the brain. As pointed out in [79],
the brain can be regarded as a complex nonlinear parallel information processing system with a concept of neuron as a basic
functional unit.
03/2010: pages 197-262;
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ABSTRACT: Can we understand the dynamic behaviour of leaky integrate-and-fire (LIF) networks, which present the major, and possibly the only, analytically tractable tool we employ in computational neuroscience? To answer this question, here we present a theoretical framework on the spike activities of LIF networks by including the first order moment (mean firing rate) and the second order moment statistics (variance and correlation), based on a moment neuronal network (MNN) approach. The spike activity of a LIF network is approximated as a Gaussian random field and can reduce to the classical Wilson-Cowan-Amari (WCA) neural field if the variances vanish. Our analyses reveal several interesting phenomena of LIF networks. With a small clamped correlation and strong inhibition, the firing rate response function could be non-monotonic (not sigmoidal type), which can lead to interesting dynamics. For a feedforward and recurrent neuronal network, our setup allows us to prove that all neuronal spike activities rapidly synchronize, a well-known fact observed in both experiments and numerical simulations. We also present several examples of wave propagations in this field model. Finally, we test our MNN with the content-dependent working memory setting. The potential application of this random neuronal field idea to account for many experimental data is also discussed.
NeuroImage 03/2010; 52(3):913-33. · 5.89 Impact Factor
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ABSTRACT: In this paper, we study cluster synchronization in networks of coupled nonidentical dynamical systems. The vertices in the same cluster have the same dynamics of uncoupled node system but the uncoupled node systems in different clusters are different. We present conditions guaranteeing cluster synchronization and investigate the relation between cluster synchronization and the unweighted graph topology. We indicate that two conditions play key roles for cluster synchronization: the common intercluster coupling condition and the intracluster communication. From the latter one, we interpret the two cluster synchronization schemes by whether the edges of communication paths lie in inter- or intracluster. By this way, we classify clusters according to whether the communications between pairs of vertices in the same cluster still hold if the set of edges inter- or intracluster edges is removed. Also, we propose adaptive feedback algorithms to adapting the weights of the underlying graph, which can synchronize any bi-directed networks satisfying the conditions of common intercluster coupling and intracluster communication. We also give several numerical examples to illustrate the theoretical results.
Chaos (Woodbury, N.Y.) 03/2010; 20(1):013120. · 1.80 Impact Factor
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ABSTRACT: We study consensus in networks of multiagents with stochastically switching topologies, where the switching topologies are described as an adapted process, a rather general process including the independent and identically distributed (i.i.d.) process and the Markov process as special cases. First, motivated by some works done in the field of stochastic stability theory, we introduce a new concept of consensus, ¿L<sub>p</sub> consensus¿ with p¿1. Then sufficient conditions for a network with stochastically switching topologies to reach L<sub>p</sub> consensus are derived for both discrete-time and continuous-time cases. In the discrete-time case, we show that the existence of a spanning tree in the conditional expectation of the union of the graphes of the network topologies across each T-length time interval for some T > 0 is sufficient for L<sub>p</sub> consensus of the network. In the continuous-time case, we also give a similar sufficient condition involving the existence of a spanning tree. As direct consequences of the main results we also give some corollaries for two important stochastic processes: the i.i.d. process and homogenous Markov process. Moreover, we compare our results with the results existing in literatures.
Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on; 01/2010
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International Joint Conference on Neural Networks, IJCNN 2010, Barcelona, Spain, 18-23 July, 2010; 01/2010
