Related papers: Reaction-Diffusion Systems as Complex Networks
The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Recently, mechanical…
We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different…
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…
Long range connections play an essential role in dynamical processes on networks, on the processing of information in biological networks, on the structure of social and economical networks and in the propagation of opinions and epidemics.…
The first goal of this article is to introduce a new type of p-adic reaction-diffusion cellular neural network with delay. We study the stability of these networks and provide numerical simulations of their responses. The second goal is to…
Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's…
In the study of reaction networks and the polynomial dynamical systems that they generate, special classes of networks with important properties have been identified. These include reversible, weakly reversible}, and, more recently,…
We study the effects of fast spatial movement of molecules on the dynamics of chemical species in a spatially heterogeneous chemical reaction network using a compartment model. The reaction networks we consider are either single- or…
Q-conditional symmetries (nonclassical symmetries) for the general class of two-component reaction-diffusion systems with non-constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first…
Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networks, such as transport processes or epidemic outbreaks. In most cases, however, they have been studied from a fermionic perspective, in which…
Networked dynamical systems, i.e., systems of dynamical units coupled via nontrivial interaction topologies, constitute models of broad classes of complex systems, ranging from gene regulatory and metabolic circuits in our cells to…
In this paper, we are concerned with the state feedback stabilization of ODE-PDE cascade systems governed by a linear ordinary differential equation and the 1-d reaction-diffusion equation posed on a bounded interval. In contrast to the…
The ability to achieve coordinated behavior --engineered or emergent-- on networked systems has attracted widespread interest over several fields. This has led to remarkable advances on the development of a theoretical understanding of the…
We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…
Adaptive networks have been recently introduced in the context of disease propagation on complex networks. They account for the mutual interaction between the network topology and the states of the nodes. Until now, existing models have…
Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…
Various disasters stem from minor perturbations, such as the spread of infectious diseases, cascading failure in power grids, etc. Analyzing perturbations is crucial for both theoretical and application fields. Previous researchers have…
This paper explores the efficacy of diffusion-based generative models as neural operators for partial differential equations (PDEs). Neural operators are neural networks that learn a mapping from the parameter space to the solution space of…
Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic…
The Comments are devoted to the paper ``Solutions of Multitime Reaction-Diffusion PDE'' (Mathematics, vol. 10 (2022), 3623), in which main results are misleading and can be derived in a simple way from those obtained earlier. Moreover, it…