Evolution of reaction-diffusion patterns in infinite and bounded domains

Wavefronts in time-delayed reaction-diffusion systems. Theory and comparison to experiment

“…We now introduce (z) = 1−n(z) > 0 and f (n) −f (1)(1−n) = |f (1)| , assuming f (1) < 0 (in biological applications f (n) is always to observed to satisfy this condition [38]). The linearized equation (75) near n = 1 is…”

Control of reactant flow at the boundary: Its effect on the onset of nonequilibrium macroscopic structures in chemical reactions

“…17 Boundary conditions ͑b.c.͒ have been recently shown to play a relevant role in the appearance and stability ͑both linear and nonlin-ear͒ of stationary patterns in bistable reaction-diffusion systems like the Schlögl model or the FitzHugh-Nagumo equations. [18][19][20][21][22][23] The most general homogeneous b.c. are partially reflecting boundary conditions ͑''albedo b.c.…”

“…in pattern selection, and more particularly with the stability properties of the resulting nonequilibrium structures. [18][19][20][21][22][23]25 Here we want to analyze how a controlled flux of a chemical species alters the parameter region of stability of the homogeneous solution that lies in the thermodynamical branch in an excitable chemical reaction. The possibility of advancing or retarding the formation of a nonequilibrium macroscopic structure by means of a change in the albedo parameter is discussed.…”

Diffusive feed of reactants and Hopf bifurcations in an oscillatory reaction-diffusion model

“…23 Moreover, there are reports on the influence of the borders on the selec-tion and orientation of dissipative structures in RD systems. 11,[24][25][26] Of particular interest are the partially reflecting boundary conditions ͑''albedo BCs''͒, that at the boundary ⌫ relate the normal derivative of the concentrations with its value:…”

“…Since these BCs are closely related to diffusion processes, it is our hope that they could be realized in experiments conducted in the new unstirred open reactors ͑e.g., in a gel ribbon or annulus͒. 27 These BCs have recently been shown to play a relevant role in the appearance and stability ͑both linear and nonlinear͒ of stationary patterns in bistable RD systems like the Schlögl model, 24,25,[28][29][30][31] the FitzHugh-Nagumo equations, 32,33 excitable reactions and bimolecular isomerization process. [34][35][36] In recent papers we have been concerned with the role of partially reflecting BCs in pattern selection, and more particularly with the stability properties of the resulting nonequilibrium structures.…”