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We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.

We extend recent results [50] on the existence of global phase-locked states (GPLS) in the Kuramoto model on a complete graph to the case of a complete bipartite graph. In particular, we prove that, for the Kuramoto model on a complete bipartite graph, the value of the critical coupling coefficient can be determined by solving a system of two nonlinear… (More)

Filtering for a class of nonlinear discrete-time stochastic systems with state delays, " J. A delay-dependent approach to H filtering for stochastic delayed jumping systems with sensor nonlinearities, " Int. Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances, " Syst. filtering for uncertain differential linear… (More)

We extend two fundamental properties of positive linear time-invariant (LTI) systems to homogeneous cooperative systems. Specifically, we demonstrate that such systems are-stable, meaning that global asymptotic stability is preserved under diagonal scaling. We also show that a delayed homogeneous cooperative system is globally asymptotically stable (GAS)… (More)

This paper revisits a well-known synthesis problem in iterative learning control, where the objective is to optimize a performance criterion over a class of causal iterations. The approach taken here adopts an infinite-time setting and looks at limit behavior. The first part of the paper considers iterations without current-cycle-feedback (CCF) term. A… (More)

We prove a convergence result for the standard Kuramoto model with all-to-all coupling. Specifically, we show that the critical coupling strength associated with the onset of completely phase-locked behaviour converges in probability as the number of oscillators tends to infinity.

Preamble The use of new technology and mathematics to study the systems of nature is one of the most significant scientific trends of the century. Driven by the need for more precise scientific understand, advances in automated measurement are providing rich new sources of biological and physiological data. This data provides information with which to… (More)

— Deep brain stimulation (DBS) has been used to ameliorate essential and Parkinsonian tremor, however the detailed mechanism by which tremor reduction is achieved remains unclear. We hypothesize that DBS works by reducing time delays in the feedback paths of the motor control loops. In particular, we suggest that antidromic activation of axonal pathways… (More)

—We correct some errors in the statements and proofs presented in Section V of the above mentioned manuscript. In the recent paper [1], the results of Section V are incorrect as stated. In this brief note, we first present an example to show that the statement of Theorem 5.1 in [1] is incorrect and then state a corrected version of this result under an… (More)

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