Pankaj Mehta Dept. of Physics, Boston University, Boston, MA 02215 Abstract Many biological and physical systems exhibit population-density dependent transitions to synchronized oscillations in a process often termed “dynamical quorum sensing”. Synchronization frequently arises through chemical communication via signaling molecules distributed through an external media. We study a simple theore...

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to...

For biological populations with nonoverlapping generations, population growth takes place in discrete time steps and is described by difference equations. Some of the simplest such nonlinear difference equations can exhibit a remarkrible spectrum of dynamical behavior, from stable equilibrium points, to stable cyclic oscillations between two population points, to stable cycles with four points,...

In this paper, we investigate a Lotka-Volterra system under regime switching dx(t) = diag(x1(t), . . . , xn(t))[(b(r(t)) + A(r(t))x(t))dt+ σ(r(t))dB(t)], where B(t) is a standard Brownian motion. The aim here is to find out what happens under regime switching. We first obtain the sufficient conditions for the existence of global positive solutions, stochastic permanence, extinction. We find out...

Abstract: This paper is concerned with a stochastic logistic model driven by martingales with jumps. In the model, generalized noise and jump noise are taken into account. This model is new and more feasible. The explicit global positive solution of the system is presented, and then sufficient conditions for extinction and persistence are established. The critical value of extinction, nonpersis...

When infectious disease transmission is density-dependent, the risk of infection will tend to increase with host population density. Since host defence mechanisms can be costly, individual hosts may benefit from increasing their investment in immunity in response to increasing population density. Such "density-dependent prophylaxis" (DDP) has now indeed been demonstrated experimentally in sever...

We investigate the dynamical behaviour of a simple plankton population model, which explicitly simulates the concentrations of nutrient, phytoplankton and zooplankton in the oceanic mixed layer. The model consists of three coupled ordinary differential equations. We use analytical and numerical techniques, focusing on the existence and nature of steady states and unforced oscillations (limit cy...

Mutual synchronization by exchange of chemicals is a mechanism for the emergence of collective dynamics in cellular populations. General theories exist on the transition to coherence, but no quantitative, experimental demonstration has been given. Here, we present a modeling and experimental analysis of cell-density-dependent glycolytic oscillations in yeast. We study the disappearance of oscil...

Tracking moving objects, including one's own body, is a fundamental ability of higher organisms, playing a central role in many perceptual and motor tasks. While it is unknown how the brain learns to follow and predict the dynamics of objects, it is known that this process of state estimation can be learned purely from the statistics of noisy observations. When the dynamics are simply linear wi...