In this paper we have studied the spatiotemporal behaviour of threshold coupled bistable chaotic maps. We have shown the existence of various cycles of the single map with the variation of threshold value for fixed relaxation time. The effects of variation of relaxation time on the network of threshold coupled maps are presented for different threshold values. Excess propagation through open boundaries is calculated numerically. For a network of three threshold coupled maps, the propagation of excess through open boundaries is calculated analytically. The condition for the existence of the steady state profile of the excess is calculated. The effects of random coupling on spatiotemporal synchronization of the network of threshold coupled maps are investigated. The key observation is that threshold coupling provides an annihilation method of the coexisting chaotic attractors of the local map and stabilizes it to some fixed point or periodic attractor. © 2014 The Royal Swedish Academy of Sciences.

SWARUP PORIA

Applied Mathematics

M NAG

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Properties of threshold coupled bistable maps

Physica Scripta

In this paper, we study synchronization behaviour of coupled Ricker maps over a complex network. Our complex network is dynamic as at every update we will connect a fraction of randomly chosen sites to a node instead of their nearest neighbours. Under nearest-neighbour coupling, synchronized period 2 behaviour of the network is observed for strong coupling strength for 2 < r < 4 (where r is the parameter of the local map) but no synchronized spatiotemporal fixed point is observed. Remarkable transitions to a spatiotemporally synchronized fixed point occur with the introduction of random rewiring. With random rewiring and for low values of r, the coupled system has only a synchronized fixed point at strong coupling but it has no synchronized period 2 for weak coupling. The synchronized period 2 for weak coupling and the synchronized fixed point for strong coupling are observed for high values of r. Note that for high values of r the synchronized period-2 oscillation exists for nearest neighbour as well as random coupling. Linear stability analysis of the synchronized steady-state solution is done analytically, and from the linear stability analysis, an analytic (approximate) expression for the critical coupling coefficient bifur (at which the onset of spatiotemporal synchronization occurs) is derived. We have simulated the complete nonlinear system and observe that our prediction from theoretical analysis matches very well with the numerical results. The variation of the basin of attraction of synchronized states with respect to coupling coefficient for different random rewirings is shown. We have also investigated the variation of basin size with respect to randomness p in rewiring for various coupling coefficients. The nontrivial result of the model is the existence of order at a global level although local dynamics is chaotic. © 2013 The Royal Swedish Academy of Sciences.

Spatiotemporal synchronization of coupled Ricker maps over a complex network

Synchronization of chaotic systems with on–off periodic coupling

Chaos: An Interdisciplinary Journal of Nonlinear Science

Lag synchronization and scaling of chaotic attractor in coupled system

Physical Review E

Controlling spatiotemporal chaos in chains of dissipative Kapitza pendula

Physical Review Letters

Reliable Logic Circuit Elements that Exploit Nonlinearity in the Presence of a Noise Floor

Journal	Physica Scripta
Publisher	Institute of Physics Publishing
ISSN	0031-8949
Open Access	No