The jump phenomenon associated with the dynamics of the duffing equation

Abstract

The mathematical nature of the jump phenomenon associated with the damped, harmonically forced Duffing equation is investigated, as regards the amplitude of the harmonic response of the system. The occurring discontinuities are treated as a bifurcation induced phenomenon, where the critical values of the respective control parameter are determined in relation to the solution of a cubic equation. Moreover, graphs illustrating the phenomenon, as well as bifurcation diagrams in the parameter planes of the system are presented. Finally, application of the presented analysis to phenomena of this kind as regards the behavior of living organisms is also discussed.

Keywords

• 34A34
• 34C15
• 34C23
• 70K40