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The proliferation and migration dichotomy of the tumor cell invasion is examined within a two-component continuous time random walk (CTRW) model. The balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration are derived. The transport of tumor cells is formulated in terms of the CTRW with an(More)
The front speed problem for nonuniform reaction rate and diffusion coefficient is studied by using singular perturbation analysis, the geometric approach of Hamilton-Jacobi dynamics, and the local speed approach. Exact and perturbed expressions for the front speed are obtained in the limit of large times. For linear and fractal heterogeneities, the analytic(More)
We studied the propagation of traveling fronts into an unstable state of the reaction-transport systems involving integral transport. By using a hyperbolic scaling procedure and singular perturbation techniques, we determined a Hamiltonian structure of reaction-transport equations. This structure allowed us to derive asymptotic formulas for the propagation(More)
A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of the path-integral approach, scaling procedure and the singular perturbation techniques involving the large deviations(More)
In this article we address the problem of the nonlinear interaction of subdiffusive particles. We introduce the random walk model in which statistical characteristics of a random walker such as escape rate and jump distribution depend on the mean density of particles. We derive a set of nonlinear subdiffusive fractional master equations and consider their(More)
We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW), we formulate a system of the balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration. The transport process is formulated(More)
Motivated by the experiments [Santamaria, Neuron 52, 635 (2006)10.1016/j.neuron.2006.10.025] that indicated the possibility of subdiffusive transport of molecules along dendrites of cerebellar Purkinje cells, we develop a mesoscopic model for transport and chemical reactions of particles in spiny dendrites. The communication between spines and a parent(More)
We propose a nonlinear random walk model which is suitable for the analysis of both chemotaxis and anomalous subdiffusive transport. We derive the master equations for the population density for the case when the transition rate for a random walk depends on residence time, chemotactic substance, and population density. We introduce the anomalous chemotactic(More)
We present a stochastic two-population model that describes the migration and growth of semi-sedentary foragers and sedentary farmers along a river valley during the Neolithic transition. The main idea of this paper is that random migration and transition from a sedentary to a foraging way of life, and backwards, is strongly coupled with the local crop(More)
We present and analyze a simplified stochastic αΩ−dynamo model which is designed to assess the influence of additive and multiplicative noises, non-normality of dynamo equation, and nonlinearity of the α−effect and turbulent diffusivity, on the generation of a large-scale magnetic field in the subcritical case. Our model incorporates random fluctuations in(More)