Classifying the Epilepsy Based on the Phase Space Sorted With the Radial Poincaré Sections in Electroencephalography

Background: Epilepsy is a brain disorder that changes the basin geometry of the oscillation of trajectories in the phase space. Nevertheless, recent studies on epilepsy often used the statistical characteristics of this space to diagnose epileptic seizures. Objectives: We evaluated changes caused by the seizures on the mentioned basin by focusing on phase space sorted by Poincaré sections. Materials & Methods: In this non-interventional clinical study (observational), 19 patients with generalized epilepsy were referred to the Epilepsy Department of Razavi Hospital (Mashhad, Iran) between 2018 and 2020, which their disease had been controlled after diagnosis and surgery. In evaluating the effects of this disorder on the oscillation basin of the EEG trajectories, we used the MATLAB@ R2019 software. In this computational method, we sorted the phase space reconstructed from the trajectories by using the radial Poincaré sections and then extracted a set of the geometric features. Finally, we detected the normal, pre-ictal, and ictal modes using a decision tree based on the Support Vector Machine (SVM) developed by features selected by a genetic algorithm. Results: The proposed method provided an accuracy of 94.96% for the three classes, which confirms the change in the oscillation basin of the trajectories. Analyzing the features by using t test also showed a significant difference between the three modes. Conclusion: The findings prove that epilepsy increases the oscillations basin of brain activity, but classification based on the segment cannot be applicable in clinical settings.

Bifurcations in a Pre-Stressed, Harmonically Excited, Vibro-Impact Oscillator at Subharmonic Resonances

This study investigates the behavior of a damped, inelastic, sinusoidally forced impact oscillator which has its barrier placed such that the oscillator always vibrates under compression about its subharmonic resonant frequencies. The Poincaré sections at near subharmonic resonance conditions exhibit finger-shaped chaotic attractors, similar to the strange attractor mapping of Hénon and the ones found by Holmes in his study of chaotic resonances of a buckled beam. The number of such fingers are observed to increase as the barrier distance from the equilibrium is decreased. These chaotic states are interspersed with regimes of periodic behavior, with the periodicity being in accordance with well defined period adding laws. This study also focuses on the ordered behavior of the one-impact period-[Formula: see text] orbits around the higher subharmonics of the oscillator.

Chaotic Motion of a Parametrically Excited Dielectric Elastomer

In this paper, an effort is made to study the chaotic motions of a dielectric elastomer (DE). The DE is activated by a time-dependent voltage (AC voltage), which is superimposed on a DC voltage. The Gent strain energy function is employed to model the nonlinear behavior of the elastomeric matter. The nonlinear ordinary differential equation (ODE) in terms of the stretch of the elastomer governing the motion of the system is deduced using the Euler–Lagrange method and the Rayleigh dissipation function. This ODE is solved via the use of a time integration-based solver. The bifurcation diagrams of Poincaré sections are generated to identify the chaotic domains. The largest Lyapunov exponents (LLEs) are illustrated for validation of the results obtained by the bifurcation diagrams. Various types of motion for the system are precisely discussed through the depiction of stretch-time responses, phase-plane diagrams, Poincaré sections and power spectral density (PSD) diagrams. The results reveal that the damping coefficient plays an influential role in suppressing the chaos phenomenon. Besides, the initial stretch of the elastomer could affect the chaotic interval of system parameters.

Simultaneous Resonances of Suspended Cables Subjected to Primary and Super-Harmonic Excitations in Thermal Environments

This paper concerns with a suspended cable in thermal environments under bi-frequency harmonic excitations, with a focus placed on the effect of temperature changes on one type of simultaneous resonance. First, the nonlinear equation of motion in thermal environments is obtained for the in-plane displacement of the cable. Then, the Galerkin method is employed to reduce the partial differential equation to an ordinary one. Second, based on the discretized form of the governing equation, the method of multiple scales is employed to obtain the second-order approximate solutions, with the stability characteristics determined. Third, numerical results are presented by using the perturbation method, together with numerical integration by the following means: frequency-response curves, time-displacement curves, phase-plane diagrams, and Poincare sections. The direct integration method is utilized to verify the results obtained by the perturbation method, while revealing more nonlinear dynamic behaviors induced by temperature changes. Both the softening and/or hardening behaviors, and the switching between them are observed for the cable in thermal environments. The response amplitude of the cable is very sensitive to temperature changes, but the number of circles in the phase diagrams and the number of cluster points in Poincaré sections is independent of the thermal effects in most cases. Finally, the vibration characteristics of the cable for different thermal expansion coefficients and temperature-dependent Young’s moduli are also investigated.

Chaotic Motions in Forced Mixed Rayleigh–Liénard Oscillator with External and Parametric Periodic-Excitations

This paper addresses the issue of a mixed Rayleigh–Liénard oscillator with external and parametric periodic-excitations. The Melnikov method is utilized to analytically determine the domain boundaries where horseshoe chaos appears. Routes to chaos are investigated through bifurcation structures, Lyapunov exponents, phase portraits and Poincaré sections. The effects of Rayleigh and Liénard parameters are analyzed. Results of analytical investigations are validated and complemented by numerical simulations.