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

Mahajan, Ashwini V.; Gade, Prashant M.

doi:10.1088/1742-5468/aaac55

Cited by 10 publications

(3 citation statements)

References 55 publications

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“…The transitions in delayed dynamical systems can be mapped on dynamic phase transitions in pseudo-spatiotemporal systems. For a delayed logistic map, this transition is in directed Ising universality class by Lepri [9] and later confirmed by Mahajan and Gade [10]. There are two different absorbing states in this system that are linked by symmetry.…”

Section: Introductionsupporting

confidence: 59%

Emergence of long range order for sublattice update in coupled map lattices

2019

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We study coupled map lattices in which lattice is divided into k sublattices updated sequentially. We obtain stability conditions for synchronized fixed point for any coupling. For synchronous update and nonlinear coupling, synchronized fixed point cannot be stabilized. But it is possible for a sublattice update. Novel bifurcations such as bifurcation to period-3 can be obtained in this case. Thus the phenomena which are usually not observed in coupled map lattices with synchronous dynamics can be observed with a sublattice update. We define an order parameter to quantify the transition to synchronization and observe a power law decay at the critical point. We also observe a power law decay of persistence at the critical point. The exponents change with k and approach a limiting value.

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Section: Introductionsupporting

confidence: 59%

Emergence of long range order for sublattice update in coupled map lattices

2019

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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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“…Directed percolation remains most studied and most observed universality class in this context. Even for PCPD, increasing evidence points to the possibility that for long enough simulations on large enough systems, it will be in directed percolation universality class [13,14].…”

Section: Introductionmentioning

confidence: 99%