Multimode oscillations in a coupled oscillator system with fifth-power nonlinear characteristics

Abstract

A method for obtaining stability of single and nonresonant double-mode oscillations occurring in a system of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> mutually coupled identical oscillators, is described. These oscillators are characterized by fifth-power nonlinearity. They are coupled by inductances containing resistive components (loss) in a ladder structure. Reduction of stable region of each mode with the increase of the loss is clarified for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N = 2,3,</tex> and 4 both by the theory and digital simulation.