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Routing mechanisms for stochastic networks are often designed to produce state space collapse (SSC) in a heavy-traffic limit, i.e., to confine the limiting process to a lower-dimensional subset of its full state space. In a fluid limit, a…
Noise can shape the firing behaviors of neurons. Here, we show that noise acting on the fast variable of the Hedgehog burster can tune the spike counts of bursts via the self-induced stochastic resonance (SISR) phenomenon. Using the…
Vector fields that are discontinuous on codimension-one surfaces are known as Filippov systems and can have attracting periodic orbits involving segments that are contained on a discontinuity surface of the vector field. In this paper we…
Extensive coherent control over quantum chaotic diffusion using the kicked rotor model is demonstrated and its origin in deviations from random matrix theory is identified. Further, the extent of control in the presence of external…
Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of…
The paper deals with local robust feedback synthesis for systems with multidimensional control and unknown bounded perturbations. Using V.~I.~Korobov's controllability function method, we construct a bounded control which steers an…
In this paper, we study the controllability of the two-dimensional relativistic Vlasov-Maxwell system in a torus, by means of an interior control. We give two types of results. With the geometric control condition on the control set, we…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…
One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent letter [Phys.~Rev.~Lett. 130, 020201…
Humans face the task of balancing dynamic systems near an unstable equilibrium repeatedly throughout their lives. Much research has been aimed at understanding the mechanisms of intermittent control in the context of human balance control.…
We numerically study the celebrated Kuramoto model of identical oscillators arranged on the sites of a two-dimensional periodic square lattice and subject to nearest neighbor interactions and dichotomous noise. In the nonequilibrium…
`Bursting', defined as periods of high frequency firing of a neuron separated by periods of quiescence, has been observed in various neuronal systems, both \textit{in vitro} and \textit{in vivo}. It has been associated with a range of…
We consider the problem of stochastic exit from a planar domain, whose boundary is an unstable periodic orbit, and which contains a stable periodic orbit. This problem arises when investigating the distribution of noise-induced phase slips…
Special quantum states exist which are quasiclassical quantizations of regions of phase space that are weakly chaotic. In a weakly chaotic region, the orbits are quite regular and remain in the region for some time before escaping and…
A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or…
We use conductance based neuron models and the mathematical modeling of Optogenetics to define controlled neuron models and we address the minimal time control of these affine systems for the first spike from equilibrium. We apply tools of…
The chaotic mixing by random two-body interactions of many-electron Fock states in a confined geometry is investigated numerically and compared with analytical predictions. Two distinct regimes are found in the dependence of the inverse…
We investigate shot noise for quantum dots whose classical phase space consists of both regular and chaotic regions. The noise is systematically suppressed below the universal value of fully chaotic systems, by an amount which varies with…
Undesired coupling to the surrounding environment destroys long-range correlations on quantum processors and hinders the coherent evolution in the nominally available computational space. This incoherent noise is an outstanding challenge to…