On Secondary Bifurcations for Some Nonlinear Convolution Equations

DOI10.2307/2000384zbMath0597.45016OpenAlexW4252922293MaRDI QIDQ3729565

Karl-Theodor Eisele, Michelle Schatzman, Francis Comets

Publication date: 1986

Full work available at URL: https://doi.org/10.2307/2000384

zbMATH Keywords

torusspin modelsperiodic structuresneurophysiologynonlinear convolution equationsecondary bifurcations

Mathematics Subject Classification ID

Other nonlinear integral equations (45G10) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Phase transitions (general) in equilibrium statistical mechanics (82B26) Integral operators (45P05) Abstract integral equations, integral equations in abstract spaces (45N05) Equations in function spaces; evolution equations (58D25) Physiological, cellular and medical topics (92Cxx)

Related Items (7)

Interfaces and typical Gibbs configurations for one-dimensional Kac potentials ⋮ Large deviation estimates for a conditional probability distribution. Applications to random interaction Gibbs measures ⋮ Asymptotic dynamics, non-critical and critical fluctuations for a geometric long-range interacting model ⋮ Unnamed Item ⋮ Variational description of Gibbs-non-Gibbs dynamical transitions for spin-flip systems with a Kac-type interaction ⋮ Heteroclinic solutions of a van der Waals model with infinite nonlocal interactions ⋮ Existence, uniqueness and analyticity for periodic solutions of a nonlinear convolution equation

Uses Software

• ALCON

Cites Work

• Nucleation for a long range magnetic model
• The von der Waals limit for classical systems. I.: A variational principle
• Efficient Numerical Pathfollowing Beyond Critical Points
• On the bounded solutions of a nonlinear convolution equation
• Large Scale Spatially Organized Activity in Neural Nets
• Secondary Bifurcation in Neuronal Nets
• Symmetry breaking and random waves for magnetic systems on a circle
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