Search
Search Results
-
Global Well-Posedness, Mean Attractors and Invariant Measures of Generalized Reversible Gray–Scott Lattice Systems Driven by Nonlinear Noise
The main objective of our investigation is to study the global well-posedness as well as stochastic dynamics of a class of generalized reversible...
-
Mean random attractors of stochastic lattice fractional delay Gray–Scott equations in higher moment product sequence spaces
This paper is devoted to the study of mean attractors in some higher moment product sequence spaces for a three-component reversible lattice...
-
Local controllability of the one-dimensional nonlocal Gray–Scott model with moving controls
In this paper, we prove the local controllability to positive constant trajectories of a nonlinear system of two coupled ODE equations, posed in the...
-
Bifurcation and Pattern Formation in an Activator–Inhibitor Model with Non-local Dispersal
In this paper, by approximating the non-local spatial dispersal equation by an associated reaction–diffusion system, an activator–inhibitor model...
-
Discontinuous stationary solutions to certain reaction-diffusion systems
Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann...
-
Stable and Unstable Periodic Spiky Solutions for the Gray–Scott System and the Schnakenberg System
The Hopf bifurcations for the classical Gray–Scott system and the Schnakenberg system in an one-dimensional interval are considered. For each system,...
-
Nonlinear Galerkin finite element methods for fourth-order Bi-flux diffusion model with nonlinear reaction term
A fourth-order diffusion model is presented with a nonlinear reaction term to simulate some special chemical and biological phenomenon. To obtain the...
-
Numerical simulations of reaction–diffusion systems in biological and chemical mechanisms with quartic-trigonometric B-splines
This article concerns with the numerical investigations of the reaction–diffusion systems (RDSs) arising in the study of pattern formation in...
-
Approximate Solutions for Some Reaction–Diffusion Systems with Non Integer Order
In this paper, three examples of fractional reaction–diffusion systems, including cubic autocatalytic reaction system, Glycolysis model and...
-
Can the Kuznetsov Model Replicate and Predict Cancer Growth in Humans?
Several mathematical models to predict tumor growth over time have been developed in the last decades. A central aspect of such models is the...
-
A different approach for conformable fractional biochemical reaction—diffusion models
This paper attempts to shed light on three biochemical reaction-diffusion models: conformable fractional Brusselator, conformable fractional...
-
Existence, Stability and Slow Dynamics of Spikes in a 1D Minimal Keller–Segel Model with Logistic Growth
We analyze the existence, linear stability, and slow dynamics of localized 1D spike patterns for a Keller–Segel model of chemotaxis that includes the...
-
Predicting the Emergence of Localised Dihedral Patterns in Models for Dryland Vegetation
Localised patterns are often observed in models for dryland vegetation, both as peaks of vegetation in a desert state and as gaps within a vegetated...
-
Large Amplitude Radially Symmetric Spots and Gaps in a Dryland Ecosystem Model
We construct far-from-onset radially symmetric spot and gap solutions in a two-component dryland ecosystem model of vegetation pattern formation on...
-
Non-Newtonian Flow on Homogeneous-Heterogeneous Pore-Scale Reactive Transport: A Computational Analysis
AbstractThis study presents a pore-scale model of a complex homogeneous-heterogeneous reaction. It is based on the Stokes equations,...
-
Spatial pattern formation in reaction–diffusion models: a computational approach
Reaction–diffusion equations have been widely used to describe biological pattern formation. Nonuniform steady states of reaction–diffusion models...
-
Semi-implicit Hermite–Galerkin Spectral Method for Distributed-Order Fractional-in-Space Nonlinear Reaction–Diffusion Equations in Multidimensional Unbounded Domains
In this paper, we construct an efficient Hermite–Galerkin spectral method for the nonlinear reaction–diffusion equations with distributed-order...
-
IDEA—Itinerant Dynamics with Emergent Attractors: A Neural Model for Conceptual Combination
It has been hypothesized that creative thinking arises partly from the emergence of novel conceptual combinations in the mind. Current understanding...
-
Efficient exponential Runge–Kutta methods of high order: construction and implementation
Exponential Runge–Kutta methods have shown to be competitive for the time integration of stiff semilinear parabolic PDEs. The current construction of...
-
Virtual Element Method for Solving an Inhomogeneous Brusselator Model With and Without Cross-Diffusion in Pattern Formation
The virtual element method (VEM) is a recent technology that can make use of very general polygonal/polyhedral meshes without the need to integrate...
