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Limit Cycles of the Schnakenberg Chemical Reaction Model
Dynamical systems contribute to the mathematical modeling of chemical reactions of biological or ecological phenomena producing limit cycle...
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Stability Analysis of Spike Solutions to the Schnakenberg Model with Heterogeneity on Metric Graphs
In this paper, we consider the linear stability of spiky stationary solutions on compact metric graphs for the Schnakenberg model with heterogeneity....
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Turing pattern formation on the sphere is robust to the removal of a hole
The formation of buds on the cell membrane of budding yeast cells is thought to be driven by reactions and diffusion involving the protein Cdc42....
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Structure preserving computational technique for fractional order Schnakenberg model
The current article deals with the analysis and numerical solution of fractional order Schnakenberg (S-B) model. This model is a system of...
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Nonlinear stability analysis of a chemical reaction–diffusion system
A reaction–diffusion model, known as the Sel’kov–Schnakenberg model, is considered. The nonlinear stability of the constant steady state is studied...
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Oscillatory Motions of Multiple Spikes in Three-Component Reaction–Diffusion Systems
For three specific singular perturbed three-component reaction–diffusion systems that admit N -spike solutions in one of the components on a finite...
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Boundary Conditions Cause Different Generic Bifurcation Structures in Turing Systems
Turing’s theory of morphogenesis is a generic mechanism to produce spatial patterning from near homogeneity. Although widely studied, we are still...
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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...
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Subcritical Turing patterns in hyperbolic models with cross–diffusion
This paper focuses on the role of hyperbolicity on pattern formation in the subcritical regime for a class of hyperbolic models with cross-diffusion....
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Novel Aspects in Pattern Formation Arise from Coupling Turing Reaction–Diffusion and Chemotaxis
Recent experimental studies on primary hair follicle formation and feather bud morphogenesis indicate a coupling between Turing-type diffusion driven...
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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,...
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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...
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An Analytical Studies of the Reaction- Diffusion Systems of Chemical Reactions
Reaction–diffusion systems are seen in not only many fields of science but also social behaviorus. In this work, Schnakenberg, Brusselator and...
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Analysis of pattern formation using numerical continuation
The paper deals with the issue of self-organization in applied sciences. It is particularly related to the emergence of Turing patterns. The goal is...
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Turing Pattern Formation Under Heterogeneous Distributions of Parameters for an Activator-Depleted Reaction Model
The purpose of this article is to study Turing pattern formation in one- and two-dimensional domains under heterogeneous distributions of the...
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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...
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Fixed and Distributed Gene Expression Time Delays in Reaction–Diffusion Systems
Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation...
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Localized outbreaks in an S-I-R model with diffusion
We investigate an SIRS epidemic model with spatial diffusion and nonlinear incidence rates. We show that for small diffusion rate of the infected...
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Multi-spike Patterns for the Gierer-Meinhardt Model with Heterogeneity on Y-shaped Metric Graph
In this paper, we consider the existence and the linear stability of spiky stationary solutions for the Gierer-Meinhardt model with heterogeneity on...
