Periodic solutions of nonlinear dynamical systems. Numerical computation, stability, bifurcation and transition to chaos

DOI10.1007/BFB0094521zbMath0728.34043MaRDI QIDQ1189365

Eduard Reithmeier

Publication date: 18 September 1992

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

zbMATH Keywords

stabilityperiodic solutionslimit cyclesHamiltonian systemsbifurcationsdynamical systemdiscontinuitiesclassification of singularitiesdifferentiable manifolddouble pendulumnumerical calculationmechanical engineeringexcitation model with dry frictionrailway vehicle systemtransformation to normal forms

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Stability for nonlinear problems in mechanics (70K20) Forced motions for nonlinear problems in mechanics (70K40) Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) Stability of solutions to ordinary differential equations (34D20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27) Stability theory for smooth dynamical systems (37C75) Numerical methods for ordinary differential equations (65L99) Local and nonlocal bifurcation theory for dynamical systems (37G99) Nonlinear resonances for nonlinear problems in mechanics (70K30) Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems (70-02) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02) Numerical analysis in abstract spaces (65J99)

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