Dynamic phase transition from localized to spatiotemporal chaos in coupled circle map with feedback

Sonawane, Abhijeet R.; Gade, Prashant M.

doi:10.1063/1.3556683

Cited by 7 publications

(3 citation statements)

References 45 publications

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“…We consider local persistence as an order parameter. As mentioned above, persistence has been helpful in studying transitions to a dynamically arrested state [11,42]. It is an analogue of first passage times.…”

Section: Modelmentioning

confidence: 99%

Stretched exponential dynamics of coupled logistic maps on a small-world network

Mahajan¹,

Gade²

2018

J. Stat. Mech.

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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 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 bandmerging 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 networks could be 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.

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Section: Modelmentioning

confidence: 99%

Stretched exponential dynamics of coupled logistic maps on a small-world network

Mahajan¹,

Gade²

2018

J. Stat. Mech.

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“…They gave this definition in the context of transition to an absorbing fixed-point state for coupled circle maps. For coupled circle maps, this definition generally seems to work even for maps with a delay, or maps with small-world connections [14,15].…”

Section: Introductionmentioning

confidence: 99%

Universal persistence exponent in transition to antiferromagnetic order in coupled logistic maps

Gade

Sahasrabudhe²

2013

Phys. Rev. E

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We study coupled logistic maps on a one-dimensional lattice. We coarse grain the system by labeling the local state + if the value of the variable is above the fixed point and - if the value is below the (nonzero) fixed point, x(*)=1-1/μ. We find that the system exhibits a transition from a global state, in which moving defects occur, to a global state, which is frozen in time (modulo-2). All such states display nonzero value of persistence. Besides, we also observe a state which displays long-range antiferromagnetic order. Onset of such a state is accompanied with a power-law behavior of persistence P(t) as a function of time at the critical line. Usually, persistence transitions show nonuniversal exponent. However, here persistence exponent for synchronous dynamics is 3/8 over the entire lower critical curve. This exponent is the same as one observed for asynchronous Glauber dynamics simulation of zero-temperature Ising model in one dimension. The expected value for synchronous dynamics is 3/4. We present a plausible argument for this scaling.

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“…Some coupled map lattices have been claimed to be in the universality class of Potts model [15]. Recently, Gade and coworkers have studied transition to chimera type states using persistence as an order parameter in coupled map lattice [16,17,18].…”

Section: Introductionmentioning

confidence: 99%

Transition to Coarse-Grained Order in Coupled Logistic Maps: Effect of Delay and Asymmetry

Rajvaidya¹,

Deshmukh²,

Gade³

et al. 2020

Preprint

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We study one-dimensional coupled logistic maps with delayed linear or nonlinear nearest-neighbor coupling. Taking the nonzero fixed point of the map x * as reference, we coarse-grain the system by identifying values above x * with the spin-up state and values below x * with the spin-down state. We define persistent sites at time T as the sites which did not change their spin state even once for all even times till time T . A clear transition from asymptotic zero persistence to non-zero persistence is seen in the parameter space. The transition is accompanied by the emergence of antiferromagnetic, or ferromagnetic order in space. We observe antiferromagnetic order for nonlinear coupling and even delay, or linear coupling and odd delay. We observe ferromagnetic order for linear coupling and even delay, or nonlinear coupling and odd delay. For symmetric coupling, we observe a power-law decay of persistence. The persistence exponent is close to 0.375 for the transition to antiferromagnetic order and close to 0.285 for ferromagnetic order. The number of domain walls decays with an exponent close to 0.5 in all cases as expected. The persistence decays as a stretched exponential and not a power-law at the critical point, in the presence of asymmetry.

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Dynamic phase transition from localized to spatiotemporal chaos in coupled circle map with feedback

Cited by 7 publications

References 45 publications

Stretched exponential dynamics of coupled logistic maps on a small-world network

Stretched exponential dynamics of coupled logistic maps on a small-world network

Universal persistence exponent in transition to antiferromagnetic order in coupled logistic maps

Transition to Coarse-Grained Order in Coupled Logistic Maps: Effect of Delay and Asymmetry

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