Does distribution theory contain means for extending Poincaré-Bendixson theory?

DOI10.1016/j.jmaa.2004.06.069zbMath1073.34007OpenAlexW1984504766MaRDI QIDQ1766690

Jan Melin

Publication date: 8 March 2005

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.06.069

zbMATH Keywords

distributionsPoincaré-Bendixson theorypiecewise Lipschitz systemssystems with discontinuities

Mathematics Subject Classification ID

Qualitative theory for ordinary differential equations (34C99) Discontinuous ordinary differential equations (34A36) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Applications of functional analysis to differential and integral equations (46N20)

Related Items (10)

Global dynamics of a state-dependent feedback control system ⋮ On conditions for regularity of solutions for a piecewise linear system ⋮ Optimal Management with Hybrid Dynamics—The Shallow Lake Problem ⋮ Network structure and input integration in competing firing rate models for decision-making ⋮ The Poincaré-Bendixson theorem: from Poincaré to the XXIst century ⋮ Bifurcation of limit cycles from generalized homoclinic loops in planar piecewise smooth systems ⋮ A nonsmooth two-sex population model ⋮ Global dynamics of a piece-wise epidemic model with switching vaccination strategy ⋮ Two types of limit cycles of a resonant converter modelled by a three-dimensional system ⋮ Some examples describing the need of modifying the Bendixson criterion for piecewise \(C^1\)-systems

Cites Work

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• Lyapunov functions for Lotka-Volterra predator-prey models with optimal foraging behavior
• Characterization of well-posedness of piecewise-linear systems
• Planar systems of piecewise linear differential equations with a line of discontinuity
• Periodic solutions of a switching dynamical system in the plane
• Multiple Lyapunov functions and other analysis tools for switched and hybrid systems
• Bifurcations in nonlinear discontinuous systems

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