arXiv subjects

Neelima Gupte

Publications and source records attributed to Neelima Gupte.

42 records · Page 3Linked to original sources

arXiv2002

Effect of asynchronicity on the universal behaviour of coupled map lattices

We investigate the spatiotemporal dynamics of coupled circle map lattices, evolving under synchronous (parallel) updating on one hand and asynchronous (random) updating rules on the other. Synchronous evolution of extended spatiotemporal systems, such as coupled circle map lattices, commonly yields multiple co-existing attractors, giving rise to phenomena strongly dependent on the initial lattice. By marked contrast numerical evidence here strongly indicates that asynchronous evolution eliminates most of the attractor states arising from special sets of initial conditions in synchronous systems, and tends to yield more global attractors. Thus the phenomenology arising from asynchronous evolution is more generic and robust in that it is obtained from many different classes of initial states. Further we show that in parameter regions where both asynchronous and synchronous evolution yield spatio-temporal intermittency, asynchronicity leads to better scaling behaviour.

nlin.CD↗

arXiv1999

Intermittency in Inhomogeneous Coupled Map Lattices

We study the phenomenon of intermittency in inhomogeneous lattices of coupled map where inhomogeneity appears in the form of different values of map parameters at adjacent sites.The system exhibits spatiotemporal intermittency in various regions of parameter space.We identify the types of co-dimension two bifurcations which give rise to spatio-temporal or purely spatial intermittency and study the mechanism in one case, that of synchronised fixed point Power law distributions of laminar lengths is observed in vicinity of such co-dim 2 points and the exponents fall in three ranges for three different types of bifurcations. Three of the exponents seen in this model show good agreement with those observed in fluid experiments with quasi-one dimensional geometries.

chao-dyn↗

arXiv1998

Targetting Chaos through Adaptive Control

We describe adaptive control algorithms whereby a chaotic dynamical system can be steered to a target state with desired characteristics. A specific implementation considered has the objective of directing the system to a state which is more chaotic or mixed than the uncontrolled one. This methodology is easy to implement in discrete or continuous dynamical systems. It is robust and efficient, and has the additional advantage that knowledge of the detailed behaviour of the system is not required.

chao-dyn↗

arXiv1997

Spatially Periodic Orbits in Coupled Sine Circle Maps

We study spatially periodic orbits for a coupled map lattice of sine circle maps with nearest neighbour coupling and periodic boundary conditions. The stability analysis for an arbitrary spatial period k is carried out in terms of the independent variables of the problem and the stability matrix is reduced to a neat block diagonal form. For a lattice of size kN, we show that the largest eigenvalue for the stability matrix of size $kN \times kN$ is the same as that for the basic spatial period k matrix of size $k \times k$. Thus the analysis for a kN lattice case can be reduced to that for a k lattice case. We illustrate this explicitly for a spatial period two case. Our formalism is general and can be extended to any coupled map lattice. We also obtain the stability regions of solutions which have the same spatial and temporal period numerically. Our analysis shows that such regions form a set of Arnold tongues in the $Ω-ε-K$ space. The tongues corresponding to higher spatial periods are contained within the tongues seen in the temporally periodic spatial period one or synchronised case. We find an interesting new bifurcation wherein the the spatially synchronised and temporal period one solution undergoes a bifurcation to a spatio-temporal period two travelling wave solution. The edges of the stability interval of this solution are analytically obtained.

chao-dyn↗

arXiv1995

Synchronisation in Coupled Sine Circle Maps

We study the spatially synchronized and temporally periodic solutions of a 1-d lattice of coupled sine circle maps. We carry out an analytic stability analysis of this spatially synchronized and temporally periodic case and obtain the stability matrix in a neat block diagonal form. We find spatially synchronized behaviour over a substantial range of parameter space. We have also extended the analysis to higher spatial periods with similar results. Numerical simulations for various temporal periods of the synchronized solution, reveal that the entire structure of the Arnold tongues and the devil's staircase seen in the case of the single circle map can also be observed for the synchronized coupled sine circle map lattice. Our formalism should be useful in the study of spatially periodic behaviour in other coupled map lattices.

patt-sol↗

arXiv1995

Enhancing Efficiency of Mixing in Chaotic Flows

We propose a mechanism by which the efficiency of mixing in chaotic flows can be enhanced. Our mechanism consists of introducing small changes in the system parameters in regions of phase space where the local Lyapunov exponent falls substantially below its average value. We have applied our mechanism to several typical chaotic maps and flows including a system of chemical reactions. We find that our method is quite efficient as it gives a substantial enhancement of the rate of mixing with small changes in system parameters, without disturbing the attractor significantly.

chao-dyn↗