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Predrag Cvitanovic

Publications and source records attributed to Predrag Cvitanovic.

6 recordsLinked to original sources
PubMed2003

Manipulating epileptiform bursting in the rat hippocampus using chaos control and adaptive techniques.

Epilepsy is a relatively common disease, afflicting 1%-2% of the population, yet many epileptic patients are not sufficiently helped by current pharmacological therapies. Recent reports have suggested that chaos control techniques may be useful for electrically manipulating epileptiform bursting behavior in vitro and could possibly lead to an alternative method for preventing seizures. We implemented chaos control of spontaneous bursting in the rat hippocampal slice using robust control techniques: stable manifold placement (SMP) and an adaptive tracking (AT) algorithm designed to overcome nonstationarity. We examined the effect of several factors, including control radius size and synaptic plasticity, on control efficacy. AT improved control efficacy over basic SMP control, but relatively frequent stimulation was still necessary and very tight control was only achieved for brief stretches. A novel technique was developed for validating period-1 orbit detection in noisy systems by forcing the system directly onto the period-1 orbit. This forcing analysis suggested that period-1 orbits were indeed present but that control would be difficult because of high noise levels and nonstationarity. Noise might actually be lower in vivo, where regulatory inputs to the hippocampus are still intact. Thus, it may still be feasible to use chaos control algorithms for preventing epileptic seizures.

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PubMed2002

Identification of determinism in noisy neuronal systems.

Most neuronal ensembles are nonlinear excitable systems. Thus it is becoming common to apply principles derived from nonlinear dynamics to characterize neuronal systems. One important characterization is whether such systems contain deterministic behavior or are purely stochastic. Unfortunately, many methods used to make this distinction do not perform well when both determinism and high-amplitude noise are present which is often the case in physiological systems. Therefore, we propose two novel techniques for identifying determinism in experimental systems. The first, called short-time expansion analysis, examines the expansion rate of small groups of points in state space. The second, called state point forcing, derives from the technique of chaos control. The system state is forced onto a fixed point, and the subsequent behavior is analyzed. This technique can be used to verify the presence of fixed points (or unstable periodic orbits) and to assess stationarity. If these are present, it implies that the system contains determinism. We demonstrate the use and possible limitations of these two techniques in two systems: the Hénon map, a classic example of a chaotic system, and spontaneous epileptiform bursting in the rat hippocampal slice. Identifying the presence of determinism in a physiological system assists in the understanding of the system's dynamics and provides a mechanism for manipulating this behavior.

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PubMed1993

A Fredholm determinant for semiclassical quantization.

We investigate a new type of approximation to quantum determinants, the "quantum Fredholm determinant," and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larger domain of analyticity and better convergence than the Gutzwiller-Voros zeta functions derived from the Gutzwiller trace formula. The conjecture is supported by numerical investigations of the 3-disk repeller, a normal-form model of a flow, and a model 2-D map.

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PubMed1992

Periodic orbit quantization of the anisotropic Kepler problem.

The periodic orbit quantization on the anisotropic Kepler problem is tested. By computing the stability and action of some 2000 of the shortest periodic orbits, the eigenvalue spectrum of the anisotropic Kepler problem is calculated. The aim is to test the following claims for calculating the quantum spectrum of classically chaotic systems: (1) Curvature expansions of quantum mechanical zeta functions offer the best semiclassical estimates; (2) the real part of the cycle expansions of quantum mechanical zeta functions cut at appropriate cycle length offer the best estimates; (3) cycle expansions are superfluous; and (4) only a small subset of cycles (irreducible cycles) suffices for good estimates for the eigenvalues. No evidence is found to support any of the four claims.

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PubMed1992

Investigation of the Lorentz gas in terms of periodic orbits.

The diffusion constant and the Lyapunov exponent for the spatially periodic Lorentz gas are evaluated numerically in terms of periodic orbits. A symbolic description of the dynamics reduced to a fundamental domain is used to generate the shortest periodic orbits. Applied to a dilute Lorentz gas with finite horizon, the theory works well, but for the dense Lorentz gas the convergence is hampered by the strong pruning of the admissible orbits.

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