Abstract
Abstract In this communication, we mainly focus our attention on the global dynamical behavior of forced and nonlinearly damped pendulum. We consider the nonlinear damping term proportional to the power of velocity (v|v| p−1). Analytically we obtain the threshold condition for the occurrence of homoclinic bifurcation using Melnikov technique. We carry out the bifurcation analysis to identify the route to chaos for various cases of damping (p = 1, 2 and 3) and analyze the topological shape and fractalness of phase space attractor by computing Kaplan-Yorke dimension and Correlation dimension. We identify the regions of 2D parameter space (consists of external forcing amplitude and damping coefficient) corresponding to various types of asymptotic dynamics through extensive Lyapunov exponent calculation and analyze the fragileness and globalness of chaos in the parameter space with the introduction of nonlinear damping. We also analyze the complexity of basin of attraction for all three cases (p = 1, 2 and 3) and compute the correlation dimension to quantify the fractalness of basin boundaries.
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