This paper studies the problem of output regulation for a class of nonlinear systems experiencing matched input disturbances. It is assumed that the disturbance signal is generated by an external autonomous dynamical system. First, we show that for a class of nonlinear systems admitting a finite-dimensional Koopman representation, the problem is equivalent to a bilinear output regulation. We then prove that a linear dynamic output feedback controller, inspired by the linear output regulation framework, locally solves the original nonlinear problem. Numerical results validate our analysis.@en

The brain consists not only of neurons but also of non-neuronal cells, including astrocytes. Recent discoveries in neuroscience suggest that astrocytes directly regulate neuronal activity by releasing gliotransmitters such as glutamate. In this paper, we consider a biologically plausible mathematical model of a tripartite neuron-astrocyte network. We study the stability of the nonlinear astrocyte dynamics, as well as its role in regulating the firing rate of the postsynaptic neuron. We show that astrocytes enable storing neuronal information temporarily. Motivated by recent findings on the role of astrocytes in explaining mechanisms of working memory, we numerically verify the utility of our analysis in showing the possibility of two competing theories of persistent and sparse neuronal activity of working memory.

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This article studies stochastic relative phase stability, i.e., stochastic phase-cohesiveness, of discrete-time phase-coupled oscillators. The stochastic phase-cohesiveness in two types of networks is studied. First, we consider oscillators coupled with 2π-periodic odd functions over underlying undirected graphs subject to both multiplicative and additive stochastic uncertainties. We prove stochastic phase-cohesiveness of the network with respect to two specific, namely, in-phase and antiphase, sets by deriving sufficient coupling conditions. We show the dependency of these conditions on the size of the mean values of additive and multiplicative uncertainties, as well as the sign of the mean values of multiplicative uncertainties. Furthermore, we discuss the results under a relaxation of the odd property of the coupling function. Second, we study an uncertain network in which the multiplicative uncertainties are governed by the Bernoulli process representing the well-known Erdös-Rényi network. We assume constant exogenous frequencies and derive sufficient conditions for achieving both stochastic phase-cohesive and phase-locked solutions, i.e., stochastic phase-cohesiveness with respect to the origin. For the latter case, where identical exogenous frequencies are assumed, we prove that any positive probability of connectivity leads to phase-locking. Thorough analyses are provided, and insights obtained from stochastic analysis are discussed, along with numerical simulations to validate the analytical results.

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This article studies free recall, i.e., the reactivation of stored memory items, namely patterns , in any order, of a model of working memory. Our free recall model is based on a biologically plausible modular neural network composed of H modules, namely hypercolumns , each of which is a bundle of M minicolumns . The coupling weights and constant bias values of the network are determined by a Hebbian plasticity rule. Using techniques from nonlinear stability theory, we show that cluster synchronization is the central mechanism governing free recall of orthogonally encoded patterns. Particularly, we show that free recall's cluster synchronization is the combination of two main mechanisms: simultaneous activities of minicolumns representing an encoded pattern, i.e., within-pattern synchronization, together with time-divided activities of minicolumns representing different patterns. We characterize the coupling and bias value conditions under which cluster synchronization emerges. We also discuss the role of heterogeneous coupling weights and bias values of minicolumns' dynamics in free recall. Specifically, we compare the behaviour of two H×2 networks with identical and non-identical coupling weights and bias values. For these two networks, we obtain bounds on couplings and bias values under which both encoded patterns are recalled. Our analysis shows that having non-identical couplings and bias values for different patterns increases the possibility of their free recall. Numerical simulations are given to validate the theoretical analysis.@en