Bifurcations in continuous piecewise linear differential systems : applications to low-dimensional electronic oscillators / / Enrique Ponce, Javier Ros, and Elísabet Vela

• Record Nr.: UNISA996503551303316
• Autore: Ponce Enrique
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 3-031-21135-9
• Descrizione fisica: 1 online resource (317 pages)
• Collana: RSME Springer ; ; v.7
• Disciplina: 780
• Soggetti: Mathematics; Equacions diferencials lineals; Teoria de la bifurcació; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Contents -- Part I Introduction -- 1 From Linear to Piecewise Linear Differential Systems -- 1.1 Some Caveats About the Notation Used in the Book -- 1.2 A Short Review on Linear Systems in ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (double struck upper R squared) /StPNE pdfmark [/StBMC pdfmarkR2ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 1.2.1 Real and Distinct Eigenvalues: ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (lamda 1 not equals lamda 2) /StPNE pdfmark [/StBMC pdfmarkλ1=λ2ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 1.2.2 Complex Eigenvalues -- 1.2.3 Nonzero Double Eigenvalues: ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (lamda 1 equals lamda 2 equals lamda not equals 0) /StPNE pdfmark [/StBMC pdfmarkλ1=λ2=λ=0ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 1.2.4 A Canonical Form for Affine Systems -- 1.2.5 The Case of Vanishing Determinant -- 1.3 Degenerate Bifurcations in Planar Affine Systems -- 1.4 The One-Parameter Liénard Form -- 1.5 Computing the Exponential Matrix -- 1.6 Passing from Linear to Piecewise Linear Systems -- 1.7 Limit Cycles in a Continuous Piecewise ; Linear Worked Example -- 1.7.1 The Right Half-Return Map -- 1.7.2 The Left Half-Return Map -- 1.7.3 A Bifurcation Analysis -- 2 Preliminary Results -- 2.1 A Unified Liénard Form for Continuous Planar Piecewise Linear Systems -- 2.2 Observable Piecewise Linear Luré Systems -- 2.3 Some Generic Results About Equilibria -- 2.3.1 Observable Continuous Piecewise Linear Systems with Two Zones -- 2.3.2 Observable Symmetric Continuous Piecewise Linear Systems with Three Zones -- 2.4 Analysis of Periodic Orbits Through Their Closing Equations -- 2.4.1 Closing Equations for Observable Continuous Piecewise Linear Systems with Two Zones.; 2.4.2 Closing Equations for Symmetric Continuous Piecewise Linear Systems with Three Zones -- 2.5 Periodic Orbits and Poincaré Maps in Piecewise Linear Systems -- 2.5.1 Derivatives of Transition Maps -- 2.5.2 Poincaré Maps in Continuous Piecewise Linear Systems with Two Zones -- 2.5.3 Poincaré Maps in Continuous Piecewise Linear Systems with Three Zones -- Part II Planar Piecewise Linear Differential Systems -- 3 Analysis of Planar Continuous Systems with Two Zones -- 3.1 Equilibria in Continuous Planar Piecewise Linear Systems with Two Zones -- 3.2 Some Preliminary Results on Limit Cycles -- 3.3 The Massera's Method for Uniqueness of Limit Cycles -- 3.4 General Results About Limit Cycles -- 3.5 Refracting Systems -- 3.6 The Bizonal Focus-Center-Limit Cycle Bifurcation -- 4 First Results for Planar Continuous Systems with Three Zones -- 4.1 Limit Cycle Existence and Uniqueness -- 4.2 The Focus-Center-Limit Cycle Bifurcation for Symmetric Continuous Planar Piecewise Linear Systems with Three Zones -- 5 Boundary Equilibrium Bifurcations and Limit Cycles -- 5.1 Boundary Equilibrium Bifurcations in Systems with Two Zones -- 5.2 Boundary Equilibrium Bifurcations in Systems with Three Zones -- 5.3 Analysis of Wien Bridge Oscillators -- 5.3.1 Revisiting the Kriegsmann's Approach -- 6 An Algebraically Computable Bifurcation in Continuous Piecewise Linear Nodal Oscillators -- 6.1 Preliminary Results -- 6.2 Analysis of Equilibria and Periodic Orbits -- 6.3 An Example of Piecewise Linear Nodal van der Pol Oscillators -- 7 The Focus-Saddle Boundary Bifurcation -- 7.1 Some Results on Focus-Saddle Refracting Systems -- 7.2 Characterizing the Focus-Saddle Boundary Equilibrium Bifurcation -- 7.3 The Effect of Initial Conditions in a Memristor Oscillator -- Part III Three-Dimensional Piecewise Linear Differential Systems.; 8 The Focus-Center-Limit Cycle Bifurcation in 3D Continuous Piecewise Linear Systems with Two Zones -- 8.1 The Generic Focus-Center-Limit Cycle Bifurcation -- 8.2 The Genesis of Asymmetric Oscillations in Chua's Circuit -- 8.3 The Degenerate Focus-Center-Limit Cycle Bifurcation in Continuous Piecewise Linear Systems with Two Zones in ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (double struck upper R cubed) /StPNE pdfmark [/StBMC pdfmarkR3ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 8.4 The Degenerate Focus-Center-Limit Cycle Bifurcation in Chua's Circuit -- 9 The FCLC Bifurcation in 3D Symmetric Continuous Piecewise Linear Systems -- 9.1 The Symmetric Focus-Center-Limit Cycle Bifurcation -- 9.2 The Degenerate Focus-Center-Limit Cycle Bifurcation in Symmetric Continuous Systems with Three Zones in ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (double struck upper R cubed) /StPNE pdfmark [/StBMC pdfmarkR3ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 10 The Piecewise Linear Analogue of Hopf-pitchfork Bifurcation -- 10.1 A One-Parameter Bifurcation Analysis -- 10.2 The Degenerate PWL Hopf-Pitchfork Bifurcation -- 10.3 The Hopf-Pitchfork Bifurcation in Chua's Circuit -- 10.4 An Extended Bonhoeffer-van der Pol Oscillator -- 11 Afterword -- A The Piecewise Linear Characteristics of Chua's Diode -- B The Chua's Oscillator -- C Some ; Auxiliary Results -- Bibliography.