Sentence examples for system with diffusion from inspiring English sources

In Section 3, we consider the system with diffusion.

In this study, we studied a nonlinear dynamics of a phytoplankton-zooplankton system with diffusion in detail.

Predator-prey systems with diffusion term may exhibit richer dynamical properties, including Turing instability, pattern formation, spatially inhomogeneous periodic solutions etc. [27 31].

In population dynamics, Lotka-Volterra competitive, cooperative, and competitive-cooperative systems with diffusion have received great attention and have been studied extensively [1 7].

In recent years, since predators and their preys distribute inhomogeneously in different spatial locations at time t, many researchers have studied predator-prey systems with diffusion term.

In this paper we prove controllability for the following reaction-diffusion system with cross diffusion matrix: (1.1).

We prove the interior approximate controllability for the following reaction-diffusion system with cross-diffusion matrix in, in,, on,,,, where is a bounded domain in,, the diffusion matrix has semisimple and positive eigenvalues, is an arbitrary constant, is an open nonempty subset of, denotes the characteristic function of the set, and the distributed controls.

For example, Chen and Wang [14] studied system (1.3) with diffusion under homogeneous Neumann boundary conditions, while Peng and Wang [15] focused on system (1.3) with diffusion under homogeneous Dirichlet boundary conditions.

Characterization of various central nervous system structures with diffusion anisotropy is possible and may be useful to monitor degenerative diseases in the central nervous system.

In this paper we prove the interior approximate controllability for the following reaction-diffusion system with cross-diffusion matrix (1.1).

A general lumping analysis of a reaction system coupled with diffusion is presented.