Studying the Dynamics and Complexity of a 3D Laser Plasma System

In this paper, a 3D laser plasma interaction system is presented, analysed, and implemented. The system has two unstable equilibria, and two types of coexisting attractors in which the coexistence of two periodic orbits and the coexistence of two chaotic attractors can be clearly observed. The multistability behaviours are determined by the bifurcation diagrams, largest Lyapunov exponents, and phase spaces. Moreover, the complexity performance of the laser plasma interaction system is investigated by the contour plot of the Sample Entropy.

Multi-Chaotic Analysis of Inter-Beat (R-R) Intervals in Cardiac Signals for Discrimination between Normal and Pathological Classes

Cardiac signals have complex structures representing a combination of simpler structures. In this paper, we develop a new data analytic tool that can extract the complex structures of cardiac signals using the framework of multi-chaotic analysis, which is based on the p-norm for calculating the largest Lyapunov exponent (LLE). Appling the p-norm is useful for deriving the spectrum of the generalized largest Lyapunov exponents (GLLE), which is characterized by the width of the spectrum (which we denote by W). This quantity measures the degree of multi-chaos of the process and can potentially be used to discriminate between different classes of cardiac signals. We propose the joint use of the GLLE and spectrum width to investigate the multi-chaotic behavior of inter-beat (R-R) intervals of cardiac signals recorded from 54 healthy subjects (hs), 44 subjects diagnosed with congestive heart failure (chf), and 25 subjects diagnosed with atrial fibrillation (af). With the proposed approach, we build a regression model for the diagnosis of pathology. Multi-chaotic analysis showed a good performance, allowing the underlying dynamics of the system that generates the heart beat to be examined and expert systems to be built for the diagnosis of cardiac pathologies.

A value of damping factor in relation to the dynamic response for a plate structure

The subject of the research is the analysis of the impact of damping value on the dynamic response of plate. The work presents the areas of dynamic stability and instability for the different damping values and compared with the plate without damping. Furthermore, the nature of solution for each analyzed case was presented. Research by using the dynamic tools such as phase portraits, Poincaré maps, FFT analysis, the largest Lyapunov exponents were performed. The compatibility of the selected method of stability analysis with the Volmir criterion was also presented.

Chaos from massive deformations of Yang-Mills matrix models

We focus on an SU(N ) Yang-Mills gauge theory in 0 + 1-dimensions with the same matrix content as the bosonic part of the BFSS matrix model, but with mass deformation terms breaking the global SO(9) symmetry of the latter to SO(5) × SO(3) × ℤ2. Introducing an ansatz configuration involving fuzzy four and two spheres with collective time dependence, we examine the chaotic dynamics in a family of effective Lagrangians obtained by tracing over the aforementioned ansatz configurations at the matrix levels $$ N=\frac{1}{6} $$ N = 1 6 (n + 1)(n + 2)(n + 3), for n = 1, 2, · · · , 7. Through numerical work, we determine the Lyapunov spectrum and analyze how the largest Lyapunov exponents(LLE) change as a function of the energy, and discuss how our results can be used to model the temperature dependence of the LLEs and put upper bounds on the temperature above which LLE values comply with the Maldacena-Shenker-Stanford (MSS) bound 2πT , and below which it will eventually be violated.

Coexistence of Strange Nonchaotic Attractors in a Quasiperiodically Forced Dynamical Map

In this paper, we investigate coexisting strange nonchaotic attractors (SNAs) in a quasiperiodically forced system. We also describe the basins of attraction for coexisting attractors and identify the mechanism for the creation of coexisting attractors. We find three types of routes to coexisting SNAs, including intermittent route, Heagy–Hammel route and fractalization route. The mechanisms for the creation of coexisting SNAs are investigated by the interruption of coexisting torus-doubling bifurcations. We characterize SNAs by the largest Lyapunov exponents, phase sensitivity exponents and power spectrum. Besides, the SNAs with extremely fractal basins exhibit sensitive dependence on the initial condition for some particular parameters.

Bifurcation and Chaos of a Discrete-Time Population Model

A Leslie population model for two generations is investigated by qualitative analysis and numerical simulation. For the different parameters a and b in the model, the dynamics of the system are studied, respectively. It shows many complex dynamic behavior, including several types of bifurcations leading to chaos, such as period-doubling bifurcations and Neimark–Sacker bifurcations. With the change of parameters, attractor crises and chaotic bands with periodic windows appear. The largest Lyapunov exponents are numerically computed and can verify the rationality of the theoretical analysis.

Observation of Strange Nonchaotic Dynamics in the Frame of State-Controlled Cellular Neural Network-Based Oscillator

In this paper, the strange nonchaotic dynamics of a quasi-periodically driven state-controlled cellular neural network (SC-CNN) based on a simple chaotic circuit is investigated using hardware experiments and numerical simulations. We report here two different routes to strange nonchaotic attractors (SNAs) taken by this SC-CNN based circuit system. These routes were confirmed using rational approximation (RA) theory, finite time Lyapunov exponents, spectrum of the largest Lyapunov exponents and their variance, and phase sensitivity exponent. It is observed that the results from both computer simulations as well as laboratory experiments have spectacular resemblance.

Chaotic Behavior in Exchange Rate

In this paper, we aim to analyze the chaotic structure of the daily Euro/USD parity. The examined data covers the period of 01/01/2004 and 03/04/2018. In this context firstly, to determine chaotic behavior of daily Euro/USD rates, the BDS test was used. And following, the chaotic behavior was examined by Largest Lyapunov Exponents (LLE) and Henon Map methods. The results proved the existence of chaotic structure in the data.

Nonlinear Analysis of Temperature during Orthogonal Turning

In this paper orthogonal turning processes are analyzed for different depth of cut. The temperature during the machining is analyzed. The nonlinear dynamics of the orthogonal turning are characterized with fft, phase plane, time delay, embedding dimension and largest Lyapunov exponents. The Lyapunov exponents can be used as a dynamic stability index for the system. The largest Lyapunov exponents for two different depth of cut show the chaotic behavior of the system.