Syamal K. Dana

Extreme multistability: Attractor manipulation and robustness

The coexistence of infinitely many attractors is called extreme multistability in dynamical systems. In coupled systems, this phenomenon is closely related to partial synchrony and characterized by the emergence of a conserved quantity. We propose a general design of coupling that leads to partial synchronization, which may be a partial complete synchronization or partial antisynchronization and even a mixed state of complete synchronization and antisynchronization in two coupled systems and, thereby reveal the emergence of extreme multistability. The proposed design of coupling has wider options and allows amplification or attenuation of the amplitude of the attractors whenever it is necessary. We demonstrate that this phenomenon is robust to parameter mismatch of the coupled oscillators.

Universal occurrence of the phase-flip bifurcation in time-delay coupled systems

Recently, the phase-flip bifurcation has been described as a fundamental transition in time-delay coupled, phase-synchronized nonlinear dynamical systems. The bifurcation is characterized by a change of the synchronized dynamics from being in-phase to antiphase, or vice versa; the phase-difference between the oscillators undergoes a jump of pi as a function of the coupling strength or the time delay. This phase-flip is accompanied by discontinuous changes in the frequency of the synchronized oscillators, and in the largest negative Lyapunov exponent or its derivative. Here we illustrate the phenomenology of the bifurcation for several classes of nonlinear oscillators, in the regimes of both periodic and chaotic dynamics. We present extensive numerical simulations and compute the oscillation frequencies and the Lyapunov spectra as a function of the coupling strength. In particular, our simulations provide clear evidence of the phase-flip bifurcation in excitable laser and Fitzhugh-Nagumo neuronal models, and in diffusively coupled predator-prey models with either limit cycle or chaotic dynamics. Our analysis demonstrates marked jumps of the time-delayed and instantaneous fluxes between the two interacting oscillators across the bifurcation; this has strong implications for the performance of the system as well as for practical applications. We further construct an electronic circuit consisting of two coupled Chua oscillators and provide the first formal experimental demonstration of the bifurcation. In totality, our study demonstrates that the phase-flip phenomenon is of broad relevance and importance for a wide range of physical and natural systems.

Oscillation death in diffusively coupled oscillators by local repulsive link.

A death of oscillation is reported in a network of coupled synchronized oscillators in the presence of additional repulsive coupling. The repulsive link evolves as an averaging effect of mutual interaction between two neighboring oscillators due to a local fault and the number of repulsive links grows in time when the death scenario emerges. Analytical condition for oscillation death is derived for two coupled Landau-Stuart systems. Numerical results also confirm oscillation death in chaotic systems such as a Sprott system and the Rössler oscillator. We explore the effect in large networks of globally coupled oscillators and find that the number of repulsive links is always fewer than the size of the network.

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 evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators

We study the transition to phase synchronization in two diffusively coupled, nonidentical Chua oscillators. In the experiments, depending on the used parameterization, we observe several distinct routes to phase synchronization, including states of either in-phase, out-of-phase, or antiphase synchronization, which may be intersected by an intermediate desynchronization regime with large fluctuations of the frequency difference. Furthermore, we report the first experimental evidence of an anomalous transition to phase synchronization, which is characterized by an initial enlargement of the natural frequency difference with coupling strength. This results in a maximal frequency disorder at intermediate coupling levels, whereas usual phase synchronization via monotonic decrease in frequency difference sets in only for larger coupling values. All experimental results are supported by numerical simulations of two coupled Chua models.

Design of coupling for synchronization in time-delayed systems.

We report a design of delay coupling for targeting desired synchronization in delay dynamical systems. We target synchronization, antisynchronization, lag-and antilag-synchronization, amplitude death (or oscillation death), and generalized synchronization in mismatched oscillators. A scaling of the size of an attractor is made possible in different synchronization regimes. We realize a type of mixed synchronization where synchronization and antisynchronization coexist in different pairs of state variables of the coupled system. We establish the stability condition of synchronization using the Krasovskii-Lyapunov function theory and the Hurwitz matrix criterion. We present numerical examples using the Mackey-Glass system and a delay Rössler system.

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.

Noise-Aided Logic in an Electronic Analog of Synthetic Genetic Networks.

We report the experimental verification of noise-enhanced logic behaviour in an electronic analog of a synthetic genetic network, composed of two repressors and two constitutive promoters. We observe good agreement between circuit measurements and numerical prediction, with the circuit allowing for robust logic operations in an optimal window of noise. Namely, the input-output characteristics of a logic gate is reproduced faithfully under moderate noise, which is a manifestation of the phenomenon known as Logical Stochastic Resonance. The two dynamical variables in the system yield complementary logic behaviour simultaneously. The system is easily morphed from AND/NAND to OR/NOR logic.