Journal ArticleDOI
Bifurcation analysis of reaction-diffusion equations—III. Chemical oscillations
J.F.G. Auchmuty,Grégoire Nicolis +1 more
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This article is published in Bulletin of Mathematical Biology.The article was published on 1976-01-01. It has received 59 citations till now. The article focuses on the topics: Saddle-node bifurcation & Transcritical bifurcation.read more
Citations
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On the stability of coupled chemical oscillators
TL;DR: In this paper, the stable steady states obtained by coupling two, three and more Brusselators in parallel, in a diffusion-like manner, are discussed, and the symmetry patterns of the stable domains are analyzed.
Journal ArticleDOI
Periodic travelling waves in cyclic populations: field studies and reaction-diffusion models.
TL;DR: The notion of a wave family, and various ecologically relevant scenarios in which periodic travelling waves occur are described, and 10 research challenges in this area are proposed, five mathematical and five empirical.
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Temporal oscillations in neuronal nets
G. B. Ermentrout,Jack D. Cowan +1 more
TL;DR: It is shown that small amplitude spatially inhomogeneous standing oscillations can bifurcate from the rest state and in a periodic domain, traveling wave trains exist.
References
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Journal ArticleDOI
The Chemical Basis of Morphogenesis
TL;DR: In this article, it is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis.
Book
The Hopf Bifurcation and Its Applications
TL;DR: The Hopf bifurcation refers to the development of periodic orbits ("self-oscillations") from a stable fixed point, as a parameter crosses a critical value as mentioned in this paper.
Journal ArticleDOI
Concentration wave propagation in two-dimensional liquid-phase self-oscillating system.
TL;DR: This work deals with patterns in a thin layer of solution, in which cerium ions catalyse the oxidation of analogues of malonic acid by bromate by oscillations in the solution colour.
Journal ArticleDOI
Symmetry Breaking Instabilities in Dissipative Systems. II
Ilya Prigogine,René Lefever +1 more
TL;DR: The thermodynamic theory of symmetry breaking instabilities in dissipative systems is presented in this article, where several kinetic schemes which lead to an unstable behavior are indicated, and the role of diffusion is studied in more detailed way.
Related Papers (5)
Bifurcation analysis of nonlinear reaction-diffusion equations—I. Evolution equations and the steady state solutions
J.F.G. Auchmuty,Grégoire Nicolis +1 more