Motivated by the recent finding [N. Kumar, G.M. Viswanathan, V.M. Kenkre, Physica A 388 (2009) 3687] that the dynamics of particles undergoing density-dependent nonlinear diffusion shows sub-diffusive behaviour, we study the Turing bifurcation in a two-variable system with this kind of...

In this paper, we consider a reaction–diffusion model for the bacterial growth. Mathematical analysis on the traveling wave solutions of the model is performed. This includes traveling wave analysis and numerical simulations of wave front propagation for a special case. Specifically, we show...

Experimental observations of cell migration often describe the presence of mesoscale patterns within motile cell populations. These patterns can take the form of cells moving as aggregates or in chain-like formation. Here we present a discrete model capable of producing mesoscale patterns. These...

In this paper, we investigate the mean field games of N agents who are weakly coupled via the empirical measures. The underlying dynamics of the representative agent is assumed to be a controlled nonlinear diffusion process with variable coefficients. We show that individual optimal strategies...

Economic growth has traditionally been analyzed in the temporal domain, while the spatial dimension is captured by cross-country income differences. Data suggest great inequality in income per capita across countries, with a slight but noticeable increase over time (Acemoglu 2009). Seeking to...

An error is corrected in Yu and Phillips (2001) (Econometrics Journal, 4, 210-224) where a time transformation was used to induce Gaussian disturbances in the discrete time equivalent model. It is shown that the error process in this model is not a martingale and the Dambis, Dubins-Schwarz (DDS)...