Prodyot K. Roy

Complex dynamics in physiological systems : from heart to brain

Contents. Part I Data Analysis. A Unified Approach to Attractor Reconstruction, Louis M. Pecora et. al. Multifractal Analysis of Physiological Data: A Non-Subjective Approach, G. Ambika et. al. Direction of Information Flow Between Heart Rate, Blood Pressure and Breathing, Teodor Buchner et. al. Part II Cardiovascular Physics: Modelling. The Mathematical Modelling of Inhomogeneities in Ventricular, Tissue T.K. Shajahan et. al. Controlling Spiral Turbulence in Simulated Cardiac Tissue by Low-Amplitude Traveling Wave Stimulation, Sitabhra Sinha et. al. Suppression of Turbulent Dynamics in Models of Cardiac Tissue by Weak Local Excitations, E. Zhuchkova et. al. Synchronization Phenomena in Networks of Oscillatory and Excitable Luo-Rudy Cells, G. V. Osipov et. al. Nonlinear Oscillations in the Conduction System of the Heart - A Model, Krzysztof Grudzinski et. al. Part III Cardiovascular Physics: Data Analysis. Statistical Physics of Human Heart Rate in Health and Disease, Ken Kiyono et. al. Cardiovascular Dynamics Following Open Heart Surgery: Early Impairment and Potential for Recovery, Robert Bauernschmitt et. al. Application of Empirical Mode Decomposition to Cardiorespiratory Synchronization, Ming-Chya Wu et. al. Part IV Cognitive and Neurosciences. Brain Dynamics and Modeling in Epilepsy: Prediction and Control Studies, Leonidas Iasemidis et. al. An Expressive Body Language Underlies Drosophila Courtship Behavior, Ruedi Stoop et. al. Speech Rhythms in Children Learning Two Languages, T. Padma Subhadra et. al. The Role of Dynamical Instabilities and Fluctuations in Hearing, J. Balakrishnan et. al. Electrical Noise in Cells, Membranes and Neurons, Subhendu Ghosh et. al. Index.

Engineering generalized synchronization in chaotic oscillators

We report a method of engineering generalized synchronization (GS) in chaotic oscillators using an open-plus-closed-loop coupling strategy. The coupling is defined in terms of a transformation matrix that maps a chaotic driver onto a response oscillator where the elements of the matrix can be arbitrarily chosen, and thereby allows a precise control of the GS state. We elaborate the scheme with several examples of transformation matrices. The elements of the transformation matrix are chosen as constants, time varying function, state variables of the driver, and state variables of another chaotic oscillator. Numerical results of GS in mismatched Rössler oscillators as well as nonidentical oscillators such as Rössler and Chen oscillators are presented.

Experimental observation on the effect of coupling on different synchronization phenomena in coupled nonidentical Chua’s oscillators

Experimental results are presented on the effect of coupling on synchronization of two coupled nonidentical Chua’s oscillators. Two oscillators are coupled in unidirectional drive response mode. The driver is always kept in chaotic (single scroll, double scroll) state while the response oscillator is kept in various dynamical states as point attractor, single scroll periodic, chaotic and double scroll. The strength of coupling plays a crucial role on synchronization between the coupled oscillators. With decreasing coupling strength, two routes of transitions, one route is through lag and intermittent lag synchronization and another one is through intermittency have been observed in single scroll cases. But the situations are slightly different when the driver is double scroll chaotic. Lag synchronization and intermittent lag synchronization regimes are present in double scroll situation, but an intermediate intermittency regime between ILS and PS has also been observed.

Lag synchronization and scaling of chaotic attractor in coupled system

We report a design of delay coupling for lag synchronization in two unidirectionally coupled chaotic oscillators. A delay term is introduced in the definition of the coupling to target any desired lag between the driver and the response. The stability of the lag synchronization is ensured by using the Hurwitz matrix stability. We are able to scale up or down the size of a driver attractor at a response system in presence of a lag. This allows compensating the attenuation of the amplitude of a signal during transmission through a delay line. The delay coupling is illustrated with numerical examples of 3D systems, the Hindmarsh-Rose neuron model, the Rössler system, a Sprott system, and a 4D system. We implemented the coupling in electronic circuit to realize any desired lag synchronization in chaotic oscillators and scaling of attractors.

Chimeralike states in a network of oscillators under attractive and repulsive global coupling.

We report chimeralike states in an ensemble of oscillators using a type of global coupling consisting of two components: attractive and repulsive mean-field feedback. We identify the existence of two types of chimeralike states in a bistable Liénard system; in one type, both the coherent and the incoherent populations are in chaotic states (which we refer to as chaos-chaos chimeralike states) and, in another type, the incoherent population is in periodic state while the coherent population has irregular small oscillation. We find a metastable state in a parameter regime of the Liénard system where the coherent and noncoherent states migrate in time from one to another subpopulation. The relative size of the incoherent subpopulation, in the chimeralike states, remains almost stable with increasing size of the network. The generality of the coupling configuration in the origin of the chimeralike states is tested, using a second example of bistable system, the van der Pol-Duffing oscillator where the chimeralike states emerge as weakly chaotic in the coherent subpopulation and chaotic in the incoherent subpopulation. Furthermore, we apply the coupling, in a simplified form, to form a network of the chaotic Rössler system where both the noncoherent and the coherent subpopulations show chaotic dynamics.

Diverse routes of transition from amplitude to oscillation death in coupled oscillators under additional repulsive links.

We report the existence of diverse routes of transition from amplitude death to oscillation death in three different diffusively coupled systems, which are perturbed by a symmetry breaking repulsive coupling link. For limit-cycle systems the transition is through a pitchfork bifurcation, as has been noted before, but in chaotic systems it can be through a saddle-node or a transcritical bifurcation depending on the nature of the underlying dynamics of the individual systems. The diversity of the routes and their dependence on the complex dynamics of the coupled systems not only broadens our understanding of this important phenomenon but can lead to potentially new practical applications.

GLUING BIFURCATIONS IN CHUA OSCILLATOR

Gluing bifurcation in a modified Chuas oscillator is reported. Keeping other parameters fixed when a control parameter is varied in the modified oscillator model, two symmetric homoclinic orbits to saddle focus at origin, which are mirror images of each other, are glued together for a particular value of the control parameter. In experiments, two asymmetric limit cycles are homoclinic to the saddle focus origin for different values of the control parameter. However, imperfect gluing bifurcation has been observed, in experiments, when one stable and unstable limit cycles merge to the saddle focus origin via saddle-node bifurcation.

BURSTING NEAR HOMOCLINIC BIFURCATION IN TWO COUPLED CHUA OSCILLATORS

We report experimental observation of cycle-cycle bursting near homoclinic bifurcation in a self-oscillating Chua oscillator when it is diffusively coupled to another excitable Chua oscillator. The excitable oscillator induces an asymmetry in the self-oscillating Chua oscillator via coupling. The coupling strength controls the strength of the asymmetry that plays a key role in transition to bursting near homoclinic bifurcation.

ON COUPLED KDV EQUATIONS

Abstract We discuss two coupled KdV equations proposed by Hirota and Satsuma, and Ito. We examine the bi-Hamiltonian structure of these couples of equations and show that the hierarchy of equations can be generated using the same set of constants of motion.

Coherent libration to coherent rotational dynamics via chimeralike states and clustering in a Josephson junction array

An array of excitable Josephson junctions under a global mean-field interaction and a common periodic forcing shows the emergence of two important classes of coherent dynamics, librational and rotational motion, in the weaker and stronger coupling limits, respectively, with transitions to chimeralike states and clustered states in the intermediate coupling range. In this numerical study, we use the Kuramoto complex order parameter and introduce two measures, a libration index and a clustering index, to characterize the dynamical regimes and their transitions and locate them in a parameter plane.