Showcase of Blue Sky Catastrophes

DOI10.1142/S0218127414400033zbMath1300.34100arXiv1310.5233OpenAlexW2105663508MaRDI QIDQ2930463

Dmitry V. Turaev, Andrej L. Shil'nikov, L. P. Shil'nikov

Publication date: 19 November 2014

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.5233

zbMATH Keywords

homoclinic bifurcationsblue sky catastrophecodimension-one

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Complex behavior and chaotic systems of ordinary differential equations (34C28) Invariant manifolds for ordinary differential equations (34C45) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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Cites Work

• Unnamed Item
• Unnamed Item
• Blue sky catastrophe in relaxation systems with one fast and two slow variables
• Bifurcations and stability of families of diffeomorphisms
• The ring principle in problems of interaction between two self- oscillating systems
• Homoclinic bifurcations of periodic orbits on a route from tonic spiking to bursting in neuron models
• ON A NEW TYPE OF BIFURCATIONS ON MANIFOLDS
• Invariant two-dimensional tori, their breakdown and stochasticity
• ON SOME MATHEMATICAL TOPICS IN CLASSICAL SYNCHRONIZATION.: A TUTORIAL
• METHODS OF THE QUALITATIVE THEORY FOR THE HINDMARSH–ROSE MODEL: A CASE STUDY – A TUTORIAL
• An Index of Fixed Point Type for Periodic Orbits
• ON THE GENERATION OF A PERIODIC MOTION FROM TRAJECTORIES DOUBLY ASYMPTOTIC TO AN EQUILIBRIUM STATE OF SADDLE TYPE
• Differentiable dynamical systems
• Expanding attractors