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

S Rajasekar and V Chinnathambi

Physica A: Statistical Mechanics and its Applications, 2000, vol. 282, issue 1, 137-154

Abstract: We consider the conservative web map xn+1=yn, yn+1=−xn−Ksinyn+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.

Keywords: Web map; Anomalous diffusion; Velocity spectrum; Lévy distribution (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:282:y:2000:i:1:p:137-154

DOI: 10.1016/S0378-4371(00)00058-3

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