Normal and anomalous diffusions in web map driven by a constant external force

Abstract

We consider the conservative web map x n+1 = y n , y n+1=−x n−K siny n+Γ where Γ is the external constant force. For a range of values of K with Γ=0 the diffusion is found to be anomalous (Zaslavsky et al., Chaos 7 (1997) 159) due to the presence of accelerator mode islands. We investigate the effect of Γ on anomalous (both dispersive and enhanced) and normal diffusions for four fixed values of K. We show the occurrence of transition from anomalous to normal and vice-versa processes by varying the value of Γ from zero. We characterize the anomalous and normal dynamics using the exponents μ – describing the evolution of mean-square displacement and β – describing the evolution of variance of short time moving distance, velocity spectrum, kurtosis and propagator. The values of the exponents μ and β are found to depend strongly on the external force Γ. We show that for anomalous diffusion the probability distributions of the variables x and y are Lévy.