Biomedical subjects

Awadhesh Prasad

Publications and source records attributed to Awadhesh Prasad.

11 recordsLinked to original sources

PubMed2006

Phase-flip bifurcation induced by time delay.

We present a general bifurcation in the synchronized dynamics of time-delay-coupled nonlinear oscillators. The relative phase between the oscillators jumps from zero to pi as a function of the coupling; this phase-flip bifurcation is accompanied by a discontinuous change in the frequency of the synchronized oscillators. This phenomenon is of broad relevance, being observed in regimes of oscillator death as well as in periodic, quasiperiodic, and chaotic dynamics. Time-delay coupling is necessary for the phase-flip bifurcation. We illustrate the phenomenon, and present analytical results for paradigmatic nonlinear systems. Possible applications are discussed.

Journal Article↗

PubMed2005

Amplitude death in coupled chaotic oscillators.

Amplitude death can occur in chaotic dynamical systems with time-delay coupling, similar to the case of coupled limit cycles. The coupling leads to stabilization of fixed points of the subsystems. This phenomenon is quite general, and occurs for identical as well as nonidentical coupled chaotic systems. Using the Lorenz and Rössler chaotic oscillators to construct representative systems, various possible transitions from chaotic dynamics to fixed points are discussed.

Journal Article↗

PubMed2005

Basin bifurcations in quasiperiodically forced coupled systems.

We study the effect of quasiperiodic forcing on a system of coupled identical logistic maps. Upon a variation of system parameters, a variety of different dynamical regimes can be observed, including phenomena such as bistability and multistability. At the bifurcation to bistability, in a manner reminiscent of attractor expansion at interior crises, there is an abrupt change in the size of attractor basins. In the bistable region, attractor basins undergo additional bifurcations wherein holes and islands are created within the basins when system parameters change. These can be understood by examining critical surfaces for the coupled system.

Journal Article↗

PubMed2004

Fractalization route to strange nonchaotic dynamics.

In the fractalization route for the formation of strange nonchaotic attractors (SNA's) in quasiperiodically driven nonlinear dynamical systems, a smooth torus gradually becomes a fractal as the forcing amplitude is increased, while the Lyapunov exponent remains nonpositive. Using techniques introduced by Kim et al. to identify unstable sets in SNA's, we study torus fractalization in a sequence of approximations wherein the quasiperiodic drive is replaced by periodic forcing of increasing period. This allows us to identify an unstable set embedded in the attractor. In the periodically forced system, we show that there is a cascade of attractor merging crises, and argue that the quasiperiodic analogue of such crises causes fractalization of tori to create SNA's.

Journal Article↗

PubMed2004

Dynamical resetting of the human brain at epileptic seizures: application of nonlinear dynamics and global optimization techniques.

Epileptic seizures occur intermittently as a result of complex dynamical interactions among many regions of the brain. By applying signal processing techniques from the theory of nonlinear dynamics and global optimization to the analysis of long-term (3.6 to 12 days) continuous multichannel electroencephalographic recordings from four epileptic patients, we present evidence that epileptic seizures appear to serve as dynamical resetting mechanisms of the brain, that is the dynamically entrained brain areas before seizures disentrain faster and more frequently (p < 0.05) at epileptic seizures than any other periods. We expect these results to shed light into the mechanisms of epileptogenesis, seizure intervention and control, as well as into investigations of intermittent spatiotemporal state transitions in other complex biological and physical systems.

Adaptation, Physiological↗

PubMed2003

Strange nonchaotic attractors in driven excitable systems.

Through quasiperiodic forcing, an excitable system can be driven into a regime of spiking behavior that is both aperiodic and stable. This is a consequence of strange nonchaotic dynamics: the motion of the system is on a fractal attractor and the largest Lyapunov exponent is negative.

Computers↗

PubMed2003

Adaptive epileptic seizure prediction system.

Current epileptic seizure "prediction" algorithms are generally based on the knowledge of seizure occurring time and analyze the electroencephalogram (EEG) recordings retrospectively. It is then obvious that, although these analyses provide evidence of brain activity changes prior to epileptic seizures, they cannot be applied to develop implantable devices for diagnostic and therapeutic purposes. In this paper, we describe an adaptive procedure to prospectively analyze continuous, long-term EEG recordings when only the occurring time of the first seizure is known. The algorithm is based on the convergence and divergence of short-term maximum Lyapunov exponents (STLmax) among critical electrode sites selected adaptively. A warning of an impending seizure is then issued. Global optimization techniques are applied for selecting the critical groups of electrode sites. The adaptive seizure prediction algorithm (ASPA) was tested in continuous 0.76 to 5.84 days intracranial EEG recordings from a group of five patients with refractory temporal lobe epilepsy. A fixed parameter setting applied to all cases predicted 82% of seizures with a false prediction rate of 0.16/h. Seizure warnings occurred an average of 71.7 min before ictal onset. Similar results were produced by dividing the available EEG recordings into half training and testing portions. Optimizing the parameters for individual patients improved sensitivity (84% overall) and reduced false prediction rate (0.12/h overall). These results indicate that ASPA can be applied to implantable devices for diagnostic and therapeutic purposes.

Algorithms↗

PubMed2003

Measuring information flow in nonlinear systems--a modeling approach in the state space.

Directional information flow between coupled nonlinear systems is of practical interest in many areas like bioengineering, chemistry, physics and electrical engineering. Due to the high complexity and nonlinearity of the coupled chaotic systems, linear modeling approaches may fail to capture the proper dynamics and thus the proper directional information flow. This necessitates novel approaches to analyze signals derived from such systems. This paper proposes a novel approach for detecting such directional information flows between the subsystems involved. The dependability of the method is illustrated using coupled chaotic oscillators in various coupling configurations.

Causality↗

PubMed2003

A new approach towards predictability of epileptic seizures: KLT dimension.

This paper proposes a measure of complexity of the epileptic electroencephalogram (EEG) based on the dimensionality of the Karhunen-Loeve Transform (KLT) in the time domain. We estimate the KLT dimensionality by assuming the same observation noise level in the EEG during the interictal period (between the seizures) as the one during an epileptic seizure (ictal period). Utilizing an optimality criterion based on the T-index [1] and the predictability time, derived from the created KLT dimensionality profiles, we show that 10 out of 15 seizures in one patient with temporal lobe epilepsy were predictable with an average predictability time of about 36 minutes.

Algorithms↗

PubMed2003

Predictability of epileptic seizures: a comparative study using Lyapunov exponent and entropy based measures.

In this paper, a comparative study involving measures from the theory of chaos, namely the short-term largest Lyapunov exponent, Shannon and Kullback-Leibler entropies from information theory, has been carried out in terms of their predictability of temporal lobe epileptic seizures. These three measures are estimated from electroencephalographic (EEG) recordings with sub-dural and in-depth electrodes from various brain locations in patients with temporal lobe epilepsy. Techniques from optimization theory are applied to select optimal sets of electrodes whose dynamics is then followed over time. Results from analysis of multiple seizures in two epileptic patients with these measures are presented and compared in terms of their ability to identify pre-ictal dynamical entrainment well ahead of seizure onset time.

Algorithms↗

PubMed2002

Unexpected robustness against noise of a class of nonhyperbolic chaotic attractors.

Chaotic attractors arising in physical systems are often nonhyperbolic. We compare two sources of nonhyperbolicity: (1) tangencies between stable and unstable manifolds, and (2) unstable dimension variability. We study the effects of noise on chaotic attractors with these nonhyperbolic behaviors by investigating the scaling laws for the Hausdorff distance between the noisy and the deterministic attractors. Whereas in the presence of tangencies, interactive noise yields attractor deformations, attractors with only dimension variability are robust, despite the fact that shadowing is grossly violated.

Journal Article↗