Although Command and Control (C2) is a complex activity, useful lessons about C2 can be learnt from simple computational models. In this paper, we describe experiments with two such models. The Kuramoto Model, though with some serious limitations, provides a representation of information flow and self-synchronization in an organization. A second (agent-based) model, based on factorization, prov...

A challenge to both understanding and modeling biochemical networks is integrating the effects of diffusion and stochasticity. Here, we use the theory of branching processes to give exact analytical expressions for the mean and variance of protein numbers as a function of time and position in a spatial version of an established model of gene expression. We show that both the mean and the magnit...

subject to appropriate initial and boundary conditions has been introduced in [15],[16] and in [23],[24] in studying phase turbulence and the flame front propagation in combustion theory. In the absence of any a priori estimates for the solutions of the scalar equation (1), most authors find it more convenient, for the mathematical study, to consider the differential form of the equation for u ...

Bursting neurons are characterized by an alternation of active and inactive state, during the active state they exhibit train of spikes and quiescent behavior in the inactive state.When bursting neurons are coupled they can synchronize depending on the coupling strength. If the coupling strength is increased above a critical value, a transition from an asynchronous state to a partial synchroniz...

A self-consistent equation to derive a discreteness-induced stochastic steady state is presented for reactiondiffusion systems. For this formalism, we use the so-called Kuramoto length, a typical distance over which a molecule diffuses in its lifetime, as was originally introduced to determine if local fluctuations influence globally the whole system. We show that this Kuramoto length is also r...

The phenomenon of self-synchronization in populations of oscillatory units appears naturally in neurosciences. However, in some situations, the formation of a coherent state is damaging. In this article we study a repulsive mean-field Kuramoto model that describes the time evolution of n points on the unit circle, which are transformed into incoherent phase-locked states. It has been recently s...

We study the impact of network heterogeneity on relaxation dynamics of the Kuramoto model on uncorrelated complex networks with scale-free degree distributions. Using the Ott-Antonsen method and the annealed-network approach, we find that the critical behavior of the relaxation rate near the synchronization phase transition does not depend on network heterogeneity and critical slowing down take...

We present synchronization and contractivity estimates for the kinetic Kuramoto model obtained from the Kuramoto phase model in the mean-field limit. For identical Kuramoto oscillators, we present an admissible class of initial data leading to time-asymptotic complete synchronization, that is, all measure valued solutions converge to the traveling Dirac measure concentrated on the initial avera...