scholarly journals Reaction-Diffusion Systems: Nonlinear Dynamics in Nature and Life. Non-equilibrium Chemical Reactions under Open Conditions.

2001 ◽  
Vol 121 (4) ◽  
pp. 243-247
Author(s):  
TOMOHIKO YAMAGUCHI
Keyword(s):  
Nonlinear Dynamics ◽  
Chemical Reactions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Equilibrium Chemical ◽  
Non Equilibrium

Re-Entrant Hexagons and Locked Turing–Hopf Fronts in the CIMA Reaction

1998 ◽  
Vol 08 (05) ◽  
pp. 1003-1012 ◽  
Author(s):  
E. Mosekilde ◽  
F. Larsen ◽  
G. Dewel ◽  
P. Borckmans
Keyword(s):  
Reaction Diffusion ◽  
Mode Locking ◽  
Mode Interaction ◽  
Integer Number ◽  
Reaction Diffusion Systems ◽  
Selection Processes ◽  
Diffusion Systems ◽  
Far From Equilibrium ◽  
Equilibrium Chemical Reaction ◽  
Equilibrium Chemical

Aspects of the mode-interaction and pattern-selection processes in far-from-equilibrium chemical reaction–diffusion systems are studied through numerical simulation of the Lengyel–Epstein model. By varying the feed concentrations, a transition is observed in which hexagons are replaced by stripes and these again by inverted hexagons. The competition between Hopf oscillations and Turing stripes is investigated by following the propagation of a front connecting the two modes. In certain parameter regimes, mode-locking is found to occur. The front then moves an integer number of Turing stripes during an integer number of Hopf oscillations. This phenomenon can be seen as arising from depinning of the Turing front under influence of the Hopf mode.

scholarly journals Stationary reaction–diffusion systems in L1

2018 ◽  
Vol 28 (11) ◽  
pp. 2161-2190 ◽  
Author(s):  
El Haj Laamri ◽  
Michel Pierre
Keyword(s):  
Chemical Reactions ◽  
Existence Of Solutions ◽  
Reaction Diffusion ◽  
Systems Modeling ◽  
Main Difficulty ◽  
Accretive Operators ◽  
Abstract Result ◽  
Reaction Diffusion Systems ◽  
Cross Diffusion ◽  
Diffusion Systems

We prove existence of solutions to stationary [Formula: see text] reaction–diffusion systems where the data are in [Formula: see text] or in [Formula: see text]. We first give an abstract result where the “diffusions” are nonlinear [Formula: see text]-accretive operators in [Formula: see text] and the reactive terms are assumed to satisfy [Formula: see text] structural inequalities. It implies that the situation is controlled by an associated cross-diffusion system and provides [Formula: see text]-estimates on the reactive terms. Next we prove existence for specific systems modeling chemical reactions and which naturally satisfy less than [Formula: see text] structural (in)equalities. The main difficulty is also to obtain [Formula: see text]-estimates on the nonlinear reactive terms.

TURING PATTERNS IN GENERAL REACTION-DIFFUSION SYSTEMS OF BRUSSELATOR TYPE

2010 ◽  
Vol 12 (04) ◽  
pp. 661-679 ◽  
Author(s):  
MARIUS GHERGU ◽  
VICENŢIU RĂDULESCU
Keyword(s):  
Chemical Reactions ◽  
Diffusion Coefficients ◽  
Crucial Role ◽  
Reaction Diffusion ◽  
Turing Patterns ◽  
General Reaction ◽  
Reaction Diffusion Systems ◽  
Brusselator Model ◽  
Diffusion Systems ◽  
Superlinear Growth

We study the reaction-diffusion system [Formula: see text] Here Ω is a smooth and bounded domain in ℝN (N ≥ 1), a, b, d1, d2 > 0 and f ∈ C1[0, ∞) is a non-decreasing function. The case f(u) = u2 corresponds to the standard Brusselator model for autocatalytic oscillating chemical reactions. Our analysis points out the crucial role played by the nonlinearity f in the existence of Turing patterns. More precisely, we show that if f has a sublinear growth then no Turing patterns occur, while if f has a superlinear growth then existence of such patterns is strongly related to the inter-dependence between the parameters a, b and the diffusion coefficients d1, d2.

Complex spatio-temporal solutions in fractional reaction-diffusion systems near a bifurcation point

2018 ◽  
Vol 21 (1) ◽  
pp. 237-253 ◽  
Author(s):  
Bohdan Datsko ◽  
Vasyl Gafiychuk
Keyword(s):  
Nonlinear Dynamics ◽  
Bifurcation Point ◽  
Reaction Diffusion ◽  
Homogeneous State ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Spatio Temporal ◽  
Complex Solutions ◽  
The Given ◽  
Fractional Reaction

Abstract In this article, we study complex spatio-temporal solutions in nonlinear time-fractional reaction-diffusion systems. The main attention is paid to nonlinear dynamics near a bifurcation point. Despite the fact that the homogeneous state is stable at the parameters lower than bifurcation ones, a variety of complex solutions can also form in the subcritical domain. As an example, we consider a generalized fractional FitzHugh-Nagumo model. Depending on the given standard bifurcation parameters and the order of fractional derivative, the new types of steady auto-wave solutions in such systems have revealed. By computer simulation, it is shown that fractional reaction-diffusion possess much more complex nonlinear dynamics than their integer counterparts even at a subcritical bifurcation.

Sign in / Sign up

Export Citation Format

Share Document