Diffusion dynamics and first passage time in a two-coupled pendulum system

Abstract

We present the numerical investigation of diffusion process and features of first passage time (FPT) and mean FPT (MFPT) in a two-coupled damped and periodically driven pendulum system. The effect of amplitude of the external periodic force and phase of the force on diffusion constant, distribution of FPT, P(tFPT), and MFPT is analyzed. Normal diffusion is found. Diffusion constant is found to show power-law variation near intermittency and sudden widening crises while linear variation is observed in the quasiperiodic region. In the intermittency crisis the divergence of diffusion constant is similar to the divergence of mean bursting length. P(tFPT) of critical distances of state variable exhibit periodic multiple peaks with decaying amplitude. MFPT of critical distances also follows power-law variation. Diffusion constant and MFPT are sensitive to the phase factor of the periodic force.

Statistical Measures and Diffusion Dynamics in a Modified Chua's Circuit Equation With Multiscroll Attractors

“…Several modified Chua's circuit models have been proposed for generating multi-scroll chaotic attractors . For example, a three-segment piece-wise linear function f characterizing voltage-current characteristic of the Chua's diode in the Chua's circuit is replaced by a discontinuous function [Khibnik et al, 1993;Lamarque et al, 1999], sigmoid function [Mahla exhibit diffusion dynamics [Blackburn & Gronbech-Jensen, 1996;Popescu et al ., 1998;Harish et al ., 2002;Sakthivel & Rajasekar, 2010]. When the mean square displacement, x 2 , is proportional to t µ , µ > 0 the underlying motion is called diffusion.…”

“…The system can exhibit infinite number of scroll chaotic attractors with diffusion characteristics. In this connection we note that certain nonlinear systems with periodic potential exhibit diffusion dynamics [Blackburn & Gronbech-Jensen, 1996;Popescu et al ., 1998;Harish et al ., 2002;Sakthivel & Rajasekar, 2010]. When the mean square displacement, x 2 , is proportional to t µ , µ > 0 the underlying motion is called diffusion.…”

Synthesis, crystal structures and luminescent properties of nickel (II) and copper (II) hexaazamacrocyclic compounds with 1,3,5-benzenetricarboxylate ligands

“…Several modified Chua's circuit models have been proposed for generating multi-scroll chaotic attractors . For example, a three-segment piece-wise linear function f characterizing voltage-current characteristic of the Chua's diode in the Chua's circuit is replaced by a discontinuous function [Khibnik et al, 1993;Lamarque et al, 1999], sigmoid function [Mahla exhibit diffusion dynamics [Blackburn & Gronbech-Jensen, 1996;Popescu et al ., 1998;Harish et al ., 2002;Sakthivel & Rajasekar, 2010]. When the mean square displacement, x 2 , is proportional to t µ , µ > 0 the underlying motion is called diffusion.…”