The paper addresses the methods of description of friction-induced self-healing at the interface between two solid bodies. A macroscopic description of self-healing is based on a Turing system for the transfer of matter that leads to self-organization at the interface in the case of an unstable state. A microscopic description deals with a kinetic model of the process and entropy production dur...

The stability of a constant steady state in general reaction-diffusion activator-inhibitor model with nonlocal dispersal the activator or inhibitor is considered. It shown that Turing type instability and associated spatial patterns can be induced by fast slow diffusion, also causes but may not produce stable patterns. The existence nonconstant positive states throu...

This work focuses on the dynamics of vegetation stripes in sloped semi-arid environments presence secondary seed dispersal and inertial effects. To this aim, a hyperbolic generalization Klausmeier model that encloses advective downhill transport plant biomass is taken into account. Analytical investigations were performed to deduce wave Turing instability loci at which oscillatory stationary pa...

The problem with the analysis of noise-induced transitions between patterns in distributed stochastic systems is considered. As a key model, we use spatially extended dynamical “phytoplankton-herbivore” system diffusion. We perform parametric bifurcation this model and determine Turing instability zone, where non-homogeneous are generated by multistability deterministic coexistence several wave...

A general system of several ordinary differential equations coupled with a reaction-diffusion equation in bounded domain zero-flux boundary condition is studied the context pattern formation. These initial-boundary value problems may have regular (i.e. sufficiently smooth) stationary solutions. This class close-to-equilibrium patterns includes solutions that emerge due to Turing instability spa...

In this paper, the kinetics of a class delayed reaction-diffusion mussel-algae system under Neumann boundary conditions with half-saturation constant is studied. The global existence and priori bounds as well positive equilibrium are obtained. affects stability may result in Turing instability. When exceeds certain critical value, globally asymptotically stable which means that larger forces mu...

We extend the definition of Maslov index to a broad class non-Hamiltonian dynamical systems. To do this, we introduce family topological spaces--which call Maslov-Arnold spaces--that share key features with Lagrangian Grassmannian, and hence admit similar theory. This contains much more. construct examples, called hyperplane spaces, that are dense in larger than Grassmannian (which is submanifo...