2017/06/21 by Ashwini V. Mahajan, Prashant M. Gade
Agricultural and Biological Sciences · Computer Science · Mathematics · Physics and Astronomy · #Bounded function #Combinatorics #Condensed matter physics #Coupling (piping) #Critical line #Exponential decay #Exponential function #Frustration #Geometry #Materials science #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Phase (matter) #Phase diagram #Phase transition #Physics #Plant and animal studies #Quantum mechanics #Scaling #Statistical physics #Theoretical and Computational Physics #Topology (electrical circuits) #cond-mat.stat-mech #nlin.CD
paper · pdf · doi:10.1088/1742-5468/aaac55
12 pages, 23 figures
arxiv created 2017/06/21 · openalex created_date 2017/06/30 · openalex publication_date 2018/02/01 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/05
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>p</mml:mi> <mml:mo stretchy="false">→</mml:mo> <mml:mn>1</mml:mn> </mml:mstyle> </mml:math> . 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.