The boundary focus-saddle bifurcation in planar piecewise linear systems. application to the analysis of memristor oscillators

DOI10.1016/j.nonrwa.2018.03.011zbMath1402.34041OpenAlexW2802161381MaRDI QIDQ1644329

Elísabet Vela, Javier Ros, Enrique Ponce

Publication date: 21 June 2018

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2018.03.011

zbMATH Keywords

limit cyclesbifurcationpiecewise linear systemsqualitative theory of planar ODEs

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Discontinuous ordinary differential equations (34A36) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (16)

Existence of four-crossing-points limit cycles in planar sector-wise linear systems with saddle-saddle dynamics ⋮ Bursting oscillations with adding-sliding structures in a Filippov-type Chua's circuit ⋮ A compendium of Hopf-like bifurcations in piecewise-smooth dynamical systems ⋮ Twenty Hopf-like bifurcations in piecewise-smooth dynamical systems ⋮ The planar discontinuous piecewise linear refracting systems have at most one limit cycle ⋮ Global studies on a continuous planar piecewise linear differential system with three zones ⋮ Bursting oscillations with bifurcations of chaotic attractors in a modified Chua's circuit ⋮ The global dynamics of linear refracting systems of focus-node or center-node type ⋮ Phase portraits of planar piecewise linear refracting systems: focus-saddle case ⋮ Unnamed Item ⋮ Limit cycles and global dynamics of planar piecewise linear refracting systems of focus-focus type ⋮ Crossing periodic orbits of nonsmooth Liénard systems and applications ⋮ Limit cycles in the discontinuous planar piecewise linear systems with three zones ⋮ Limit cycles from a monodromic infinity in planar piecewise linear systems ⋮ Unnamed Item ⋮ Harmonic solutions for a class of non-autonomous piecewise linear oscillators

Cites Work

• Unnamed Item
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• Generic bifurcation of refracted systems
• A general mechanism to generate three limit cycles in planar Filippov systems with two zones
• Uniqueness of limit cycles for sewing planar piecewise linear systems
• Piecewise-smooth dynamical systems. Theory and applications
• The Focus-Center-Limit Cycle Bifurcation in Discontinuous Planar Piecewise Linear Systems Without Sliding
• On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities
• NONHYPERBOLIC BOUNDARY EQUILIBRIUM BIFURCATIONS IN PLANAR FILIPPOV SYSTEMS: A CASE STUDY APPROACH
• One-Parameter Bifurcations in Planar Filippov Systems
• Bifurcation Sets of Continuous Piecewise Linear Systems with Two Zones
• Nonlinear Dynamics of Memristor Oscillators
• Limit Cycle and Boundary Equilibrium Bifurcations in Continuous Planar Piecewise Linear Systems
• MEMRISTOR OSCILLATORS
• Canonical Discontinuous Planar Piecewise Linear Systems

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