NONAUTONOMOUS SADDLE-NODE BIFURCATION IN A CANONICAL ELECTROSTATIC MEMS

DOI10.1142/S0218127413500880zbMath1270.34125OpenAlexW2114927365MaRDI QIDQ2845304

Pedro J. Torres, Alexander J. Gutierrez

Publication date: 22 August 2013

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

Full work available at URL: https://doi.org/10.1142/s0218127413500880

zbMATH Keywords

saddle-node bifurcationperiodic solutionLeray-Schauder degreeMEMS

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Contact in solid mechanics (74M15) Stability of solutions to ordinary differential equations (34D20) Applications of operator theory to differential and integral equations (47N20) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (12)

Multiplicity of positive periodic solutions of Rayleigh equations with singularities ⋮ Global solution curves for several classes of singular periodic problems ⋮ Periodic oscillations in MEMS under squeeze film damping force ⋮ On the positive periodic solutions of a class of Liénard equations with repulsive singularities in degenerate case ⋮ Bifurcation and dynamics of periodic solutions to the Rayleigh-plesset equation: theory and numerical simulation ⋮ Periodic oscillations in electrostatic actuators under time delayed feedback controller ⋮ Analysis of dynamic pull-in voltage of a graphene MEMS model ⋮ On the stability of periodic solutions with defined sign in MEMS via lower and upper solutions ⋮ Existence and multiplicity of positive periodic solutions to Minkowski-curvature equations without coercivity condition ⋮ Odd periodic oscillations in Comb-drive finger actuators ⋮ Dynamics of periodic solution to a electrostatic micro-electro-mechanical system ⋮ A singular periodic Ambrosetti–Prodi problem of Rayleigh equations without coercivity conditions

Cites Work

• Dynamics of a canonical electrostatic MEMS/NEMS system
• Twist periodic solutions of second order singular differential equations
• Twist periodic solutions of repulsive singular equations
• Dynamics of a periodic differential equation with a singular nonlinearity of attractive type
• Twist Solutions of a Hill's Equation with Singular Term
• DYNAMICS OF ELECTROSTATICALLY ACTUATED MICRO-ELECTRO-MECHANICAL SYSTEMS: SINGLE DEVICE AND ARRAYS OF DEVICES
• INTERNAL RESONANCES AND BIFURCATIONS OF AN ARRAY BELOW THE FIRST PULL-IN INSTABILITY
• A Multiplicity Result for Periodic Solutions of Forced Nonlinear Second order Ordinary Differential Equations
• Topological Degree and Stability of Periodic Solutions for Certain Differential Equations
• BIFURCATION OF EQUILIBRIA IN MICROMACHINED ELASTIC STRUCTURES WITH ELECTROSTATIC ACTUATION
• Existence and stability of periodic solutions for second-order semilinear differential equations with a singular nonlinearity

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