arXiv subjects

Sudeshna Sinha

Publications and source records attributed to Sudeshna Sinha.

53 records · Page 3Linked to original sources

arXiv2010

Design of time delayed chaotic circuit with threshold controller

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.

nlin.CD↗

arXiv2010

A Coupled Map Lattice Model for Rheological Chaos in Sheared Nematic Liquid Crystals

A variety of complex fluids under shear exhibit complex spatio-temporal behaviour, including what is now termed rheological chaos, at moderate values of the shear rate. Such chaos associated with rheological response occurs in regimes where the Reynolds number is very small. It must thus arise as a consequence of the coupling of the flow to internal structural variables describing the local state of the fluid. We propose a coupled map lattice (CML) model for such complex spatio-temporal behaviour in a passively sheared nematic liquid crystal, using local maps constructed so as to accurately describe the spatially homogeneous case. Such local maps are coupled diffusively to nearest and next nearest neighbours to mimic the effects of spatial gradients in the underlying equations of motion. We investigate the dynamical steady states obtained as parameters in the map and the strength of the spatial coupling are varied, studying local temporal properties at a single site as well as spatio-temporal features of the extended system. Our methods reproduce the full range of spatio-temporal behaviour seen in earlier one-dimensional studies based on partial differential equations. We report results for both the one and two-dimensional cases, showing that spatial coupling favours uniform or periodically time-varying states, as intuitively expected. We demonstrate and characterize regimes of spatio-temporal intermittency out of which chaos develops. Our work suggests that such simplified lattice representations of the spatio-temporal dynamics of complex fluids under shear may provide useful insights as well as fast and numerically tractable alternatives to continuum representations.

cond-mat.soft↗

arXiv2008

Under what kind of parametric fluctuations is spatiotemporal regularity the most robust?

It was observed that the spatiotemporal chaos in lattices of coupled chaotic maps was suppressed to a spatiotemporal fixed point when some fraction of the regular coupling connections were replaced by random links. Here we investigate the effects of different kinds of parametric fluctuations on the robustness of this spatiotemporal fixed point regime. In particular we study the spatiotemporal dynamics of the network with noisy interaction parameters, namely fluctuating fraction of random links and fluctuating coupling strengths. We consider three types of fluctuations: (i) noisy in time, but homogeneous in space; (ii) noisy in space, but fixed in time; (iii) noisy in both space and time. We find that the effect of different kinds of parameteric noise on the dy- namics is quite distinct: quenched spatial fluctuations are the most detrimental to spatiotemporal regularity; spatiotemporal fluctuations yield phenomena similar to that observed when parameters are held constant at the mean-value; and interestingly, spatiotemporal regularity is most robust under spatially uniform temporal fluctuations, which in fact yields a larger fixed point range than that obtained under constant mean-value parameters.

nlin.CD↗

arXiv2008

Enhancement of spatiotemporal regularity in an optimal window of random coupling

We investigate the spatiotemporal dynamics of a lattice of coupled chaotic maps whose coupling connections are dynamically rewired to random sites with probability p, namely at any instance of time, with probability p a regular link is switched to a random one. In a range of weak coupling, where spatiotemporal chaos exists for regular lattices (i.e. for p = 0), we find that p > 0 yields synchronized periodic orbits. Further we observe that this regularity occurs over a window of p values, beyond which the basin of attraction of the synchronized cycle shrinks to zero. Thus we have evidence of an optimal range of randomness in coupling connections, where spatiotemporal regularity is efficiently obtained. This is in contrast to the commonly observed monotonic increase of synchronization with increasing p, as seen for instance, in the strong coupling regime of the very same system.

nlin.CD↗

arXiv2008

Non-universal dependence of spatiotemporal regularity on randomness in coupling connections

We investigate the spatiotemporal dynamics of a network of coupled nonlinear oscillators, modeled by sine circle maps, with varying degrees of randomness in coupling connections. We show that the change in the basin of attraction of the spatiotemporal fixed point due to varying fraction of random links $p$, is crucially related to the nature of the local dynamics. Even the qualitative dependence of spatiotemporal regularity on $p$ changes drastically as the angular frequency of the oscillators change, ranging from monotonic increase or monotonic decrease, to non-monotonic variation. Thus it is evident here that the influence of random coupling connections on spatiotemporal order is highly non-universal, and depends very strongly on the nodal dynamics.

nlin.CD↗

arXiv2008

Regular and Chaotic States in a Local Map Description of Sheared Nematic Liquid Crystals

We propose and study a local map capable of describing the full variety of dynamical states, ranging from regular to chaotic, obtained when a nematic liquid crystal is subjected to a steady shear flow. The map is formulated in terms of a quaternion parametrization of rotations of the local frame described by the axes of the nematic director, subdirector and the joint normal to these, with two additional scalars describing the strength of ordering. Our model yields kayaking, wagging, tumbling, aligned and coexistence states, in agreement with previous formulations based on coupled ordinary differential equations. Such a map can serve as a building block for the construction of lattice models of the complex spatio-temporal states predicted for sheared nematics.

cond-mat.soft↗

arXiv2005

Robust Emergent Activity in Dynamical Networks

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we develop a macroscopic description of the system in terms of the statistical features of the subnetwork of active nodes. We find the asymptotic characteristics of this subnetwork to be remarkably robust: the size of the active set is independent of the total number of nodes in the network, and the average degree of the active nodes is independent of both the network size and its connectivity. These results suggest that very different networks evolve to active subnetworks with the same characteristic features. This has strong implications for dynamical networks observed in the natural world, notably the existence of a characteristic range of links per species across ecological systems.

cond-mat.stat-mech↗

arXiv2005

Dynamic Transitions in Small World Networks: Approach to Equilibrium

We study the transition to phase synchronization in a model for the spread of infection defined on a small world network. It was shown (Phys. Rev. Lett. {\bf 86} (2001) 2909) that the transition occurs at a finite degree of disorder $p$, unlike equilibrium models where systems behave as random networks even at infinitesimal $p$ in the infinite size limit. We examine this system under variation of a parameter determining the driving rate, and show that the transition point decreases as we drive the system more slowly. Thus it appears that the transition moves to $p=0$ in the very slow driving limit, just as in the equilibrium case.

cond-mat.stat-mech↗

arXiv2005

Evidence of universality for the May-Wigner stability theorem for random networks with local dynamics

We consider a random network of nonlinear maps exhibiting a wide range of local dynamics, with the links having normally distributed interaction strengths. The stability of such a system is examined in terms of the asymptotic fraction of nodes that persist in a non-zero state. Scaling results show that the probability of survival in the steady state agrees remarkably well with the May-Wigner stability criterion derived from linear stability arguments. This suggests universality of the complexity-stability relation for random networks with respect to arbitrary global dynamics of the system.

nlin.AO↗

arXiv2004

A q-deformed nonlinear map

A scheme of q-deformation of nonlinear maps is introduced. As a specific example, a q-deformation procedure related to the Tsallis q-exponential function is applied to the logistic map. Compared to the canonical logistic map, the resulting family of q-logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors -- a phenomenon rare in one dimensional maps.

nlin.CD↗

arXiv2004

How Crucial is Small World Connectivity for Dynamics?

We study the dynamical behaviour of the collective field of chaotic systems on small world lattices. Coupled neuronal systems as well as coupled logistic maps are investigated. We observe that significant changes in dynamical properties occur only at a reasonably high strength of nonlocal coupling. Further, spectral features, such as signal-to-noise ratio (SNR), change monotonically with respect to the fraction of random rewiring, i.e. there is no optimal value of the rewiring fraction for which spectral properties are most pronounced. We also observe that for small rewiring, results are similar to those obtained by adding small noise.

nlin.CD↗

arXiv2002

Persistence at the onset of spatiotemporal intermittency in coupled map lattices

We study persistence in coupled circle map lattices at the onset of spatiotemporal intermittency, an onset which marks a continuous transition, in the universality class of directed percolation, to a unique absorbing state. We obtain a local persistence exponent of theta_l = 1.49 +- 0.02 at this transition, a value which closely matches values for theta_l obtained in stochastic models of directed percolation. This result constitutes suggestive evidence for the universality of persistence exponents at the directed percolation transition. Given that many experimental systems are modelled accurately by coupled map lattices, experimental measurements of this persistence exponent may be feasible.

cond-mat.stat-mech↗

arXiv2002

Evidence for directed percolation universality at the onset of spatiotemporal intermittency in coupled circle maps

We consider a lattice of coupled circle maps, a model arising naturally in descriptions of solid state phenomena such as Josephson junction arrays. We find that the onset of spatiotemporal intermittency (STI) in this system is analogous to directed percolation (DP), with the transition being to an unique absorbing state for low nonlinearities, and to weakly chaotic absorbing states for high nonlinearities. We find that the complete set of static exponents and spreading exponents at all critical points match those of DP very convincingly. Further, hyperscaling relations are fulfilled, leading to independent controls and consistency checks of the values of all the critical exponents. These results lend strong support to the conjecture that the onset of STI in deterministic models belongs to the DP universality class.

nlin.CD↗

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↗

arXiv2002

Random Coupling of Chaotic Maps leads to Spatiotemporal Synchronisation

We investigate the spatiotemporal dynamics of a network of coupled chaotic maps, with varying degrees of randomness in coupling connections. While strictly nearest neighbour coupling never allows spatiotemporal synchronization in our system, randomly rewiring some of those connections stabilises entire networks at $x^*$, where $x^*$ is the strongly unstable fixed point solution of the local chaotic map. In fact, the smallest degree of randomness in spatial connections opens up a window of stability for the synchronised fixed point in coupling parameter space. Further, the coupling $ε_{bifr}$ at which the onset of spatiotemporal synchronisation occurs, scales with the fraction of rewired sites p as a power law, for 0.1 < p < 1. We also show that the regularising effect of random connections can be understood from stability analysis of the probabilistic evolution equation for the system, and approximate analytical expressions for the range and $ε_{bifr}$ are obtained.

nlin.CD↗

arXiv1999

Distribution of Husimi Zeroes in Polygonal Billiards

The zeroes of the Husimi function provide a minimal description of individual quantum eigenstates and their distribution is of considerable interest. We provide here a numerical study for pseudo- integrable billiards which suggests that the zeroes tend to diffuse over phase space in a manner reminiscent of chaotic systems but nevertheless contain a subtle signature of pseudo-integrability. We also find that the zeroes depend sensitively on the position and momentum uncertainties with the classical correspondence best when the position and momentum uncertainties are equal. Finally, short range correlations seem to be well described by the Ginibre ensemble of complex matrices.

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↗