Stretched exponential dynamics of coupled logistic maps on a small-world network. (27th February 2018)

• Record Type: Journal Article
• Authors: Mahajan, Ashwini V; Gade, Prashant M
• Is Part Of: Journal of statistical mechanics. (2018:Feb.)
• Publication Date: 2018-02-27
• Subjects: 4 -- 12; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aaac55
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We investigate the dynamic phase transition from partially or fully arrested state to spatiotemporal chaos in coupled logistic maps on a small-world network. Persistence of local variables in a coarse grained sense acts as an excellent order parameter to study this transition. We investigate the phase diagram by varying coupling strength and small-world rewiring probability p of nonlocal connections. The persistent region is a compact region bounded by two critical lines where band-merging crisis occurs. On one critical line, the persistent sites shows a nonexponential (stretched exponential) decay for all p while for another one, it shows crossover from nonexponential to exponential behavior as p → 1 . With an effectively antiferromagnetic coupling, coupling to two neighbors on either side leads to exchange frustration. Apart from exchange frustration, non-bipartite topology and nonlocal couplings in a small-world network could be a reason for anomalous relaxation. The distribution of trap times in asymptotic regime has a long tail as well. The dependence of temporal evolution of persistence on initial conditions is studied and a scaling form for persistence after waiting time is proposed. We present a simple possible model for this behavior.