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.
In a typical perceptual identification task, a word is presented for a few milliseconds and masked; then subjects are asked to report the word. It has been found that an earlier presentation of the test word will improve identification of the test word by as much as 30%. In addition, this facilitation has been shown to be preserved under amnesia. In this… (More)
We extend recent results  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)
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)
A survey of the use of graph theoretical techniques in Biology is presented. In particular, recent work on identifying and modelling the structure of bio-molecular networks is discussed, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link… (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)
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)
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)
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.
— 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)