Related papers: Pattern control via Diffussion interaction
Dynamic phenomena in social and biological sciences can often be modeled by employing reaction-diffusion equations. When addressing the control of these modes, from a mathematical viewpoint one of the main challenges is that, because of the…
Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of…
We study diffusion-controlled processes in nonequilibrium steady states, where standard rate theory assumptions break down. Using transition path theory, we generalize the relations between reactive probability fluxes and measures of the…
Reaction-diffusion systems driven far from thermodynamic equilibrium through the injection of energy can support multiple distinct spatial patterns that persist as long-lived dynamical phases. The stability of these metastable phases is not…
This paper addresses the problem of generating dynamically admissible trajectories for control tasks using diffusion models, particularly in scenarios where the environment is complex and system dynamics are crucial for practical…
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing…
Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper we consider a class of infinite time-horizon singular stochastic control problems for…
This study explores the integration of a diffusion control parameter into the chaotic dynamics of a modified bouncing ball model. By extending beyond simple elastic collisions, the model introduces elements that affect the diffusive…
In this article we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear…
Controlling a dynamical system is the ability of changing its configuration arbitrarily through a suitable choice of inputs. It is a very well studied concept in control theory, with wide ranging applications in medicine, biology, social…
This paper investigates steady state solutions of a vasculogenesis model governed by coupled partial differential equations in a bounded two dimensional domain. Explicit steady state solutions are analytically constructed, and their…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous…
Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the…
This paper is concerned with the optimal control of hysteresis-reaction-diffusion systems. We study a control problem with two sorts of controls, namely distributed control functions, or controls which act on a part of the boundary of the…
Many biological activities are induced by cellular chemical reactions of diffusing reactants. The dynamics of such systems can be captured by stochastic reaction networks. A recent numerical study has shown that diffusion can significantly…
Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the backstepping method. The extension of this result to systems with advection terms and…