Horseshoe dynamics in Duffing oscillator with fractional damping and multi-frequency excitation

Document Type: Research Paper

Authors

1 Department of Physics, Sadakathullah Appa College, Tirunelveli-627 011, Tamil Nadu, India (Affliated to Manonmaniam Sundaranar University, Tirunelveli-627012, Tamil Nadu, India)

2 Department of Mathematics, St. Xavier's College, Tirunelveli -627 002, Tamil Nadu, India

3 School of Physics, Bharathidasan University, Tiruchirapalli-620 024, Tamil Nadu, India

10.22124/jmm.2019.12719.1242

Abstract

The occurrence of horseshoe chaos in Duffing oscillator with fractional damping and multi-frequency excitation is analyzed  by using analytical and numerical techniques. Applying Melnikov method, analytical threshold condition for the onset of horseshoe chaos is obtained. The effect of damping exponent and the number of periodic forces on the dynamics of the Duffing oscillator is also analyzed. Due to fractional damping and multi-frequency excitation, suppression of chaos and various nonlinear phenomena are predicted. Analytical predictions are demonstrated through numerical simulations.

Keywords