Jepsenswain6614

This paper presents a new five-term chaotic model derived from the Rössler prototype-4 equations. The proposed system is elegant, variable-boostable, multiplier-free, and exclusively based on a sine nonlinearity. However, its algebraic simplicity hides very complex dynamics demonstrated here using familiar tools such as bifurcation diagrams, Lyapunov exponents spectra, frequency power spectra, and basins of attraction. With an adjustable number of equilibrium, the new model can generate infinitely many identical chaotic attractors and limit cycles of different magnitudes. Its dynamic behavior also reveals up to six nontrivial coexisting attractors. Analog circuit and field programmable gate array-based implementation are discussed to prove its suitability for analog and digital chaos-based applications. Finally, the sliding mode control of the new system is investigated and simulated.Excitable media sustain circulating waves. In the heart, sustained circulating waves can lead to serious impairment or even death. To investigate factors affecting the stability of such waves, we have used optogenetic techniques to stimulate a region at the apex of a mouse heart at a fixed delay after the detection of excitation at the base of the heart. For long delays, rapid circulating rhythms can be sustained, whereas for shorter delays, there are paroxysmal bursts of activity that start and stop spontaneously. By considering the dependence of the action potential and conduction velocity on the preceding recovery time using restitution curves, as well as the reduced excitability (fatigue) due to the rapid excitation, we model prominent features of the dynamics including alternation of the duration of the excited phases and conduction times, as well as termination of the bursts for short delays. We propose that this illustrates universal mechanisms that exist in biological systems for the self-termination of such activities.We present a new four-step feedback procedure to study the full dynamics of a nonlinear dynamical system, namely, the logistic map. We show that by using this procedure, the chaotic behavior of the logistic map can be controlled easily and rapidly or the system can be made stable for higher values of the population growth parameter. We utilize various dynamical techniques (orbit evolution, time series analysis, bifurcation diagrams, and Lyapunov exponents) to analyze the dynamics of the logistic map. Additionally, we adopt the switching strategy to control chaos or to increase the stability performance of the logistic map. Finally, we propose a modified traffic control model to enable rapid control of unexpected traffic on the road. The results of this model are supported by a physical interpretation. The model is found to be more efficient than existing models of Lo and Cho [J. Franklin Inst. 342, 839-851 (2005)] and Ashish et al. [Nonlinear Dyn. 94, 959-975 (2018)]. This work provides a novel feedback procedure that facilitates rapid control of chaotic behavior and increases the range of stability of dynamical systems.We present an integrated approach to analyze the multi-lead electrocardiogram (ECG) data using the framework of multiplex recurrence networks (MRNs). We explore how their intralayer and interlayer topological features can capture the subtle variations in the recurrence patterns of the underlying spatio-temporal dynamics of the cardiac system. We find that MRNs from ECG data of healthy cases are significantly more coherent with high mutual information and less divergence between respective degree distributions. In cases of diseases, significant differences in specific measures of similarity between layers are seen. The coherence is affected most in the cases of diseases associated with localized abnormality such as bundle branch block. We note that it is important to do a comprehensive analysis using all the measures to arrive at disease-specific patterns. Our approach is very general and as such can be applied in any other domain where multivariate or multi-channel data are available from highly complex systems.I present a systematic evaluation of different types of metrics, for inferring magnitude, amplitude, or phase synchronization from the electroencephalogram (EEG) and the magnetoencephalogram (MEG). I used a biophysical model, generating EEG/MEG-like signals, together with a system of two coupled self-sustained chaotic oscillators, containing clear transitions from phase to amplitude synchronization solely modulated by coupling strength. Specifically, I compared metrics according to five benchmarks for assessing different types of reliability factors, including immunity to spatial leakage, test-retest reliability, and sensitivity to noise, coupling strength, and synchronization transition. My results delineate the heterogeneous reliability of widely used connectivity metrics, including two magnitude synchronization metrics [coherence (Coh) and imaginary part of coherence (ImCoh)], two amplitude synchronization metrics [amplitude envelope correlation (AEC) and corrected amplitude envelope correlation (AECc)], and three phase synchronization metrics [phase coherence (PCoh), phase lag index (PLI), and weighted PLI (wPLI)]. First, the Coh, AEC, and PCoh were prone to create spurious connections caused by spatial leakage. Therefore, they are not recommended to be applied to real EEG/MEG data. The ImCoh, AECc, PLI, and wPLI were less affected by spatial leakage. The PLI and wPLI showed the highest immunity to spatial leakage. Second, the PLI and wPLI showed higher test-retest reliability and higher sensitivity to coupling strength and synchronization transition than the ImCoh and AECc. Third, the AECc was less noisy than the ImCoh, PLI, and wPLI. In sum, my work shows that the choice of connectivity metric should be determined after a comprehensive consideration of the aforementioned five reliability factors.We define the class of multivariate group entropies as a novel set of information-theoretical measures, which extends significantly the family of group entropies. check details We propose new examples related to the "super-exponential" universality class of complex systems; in particular, we introduce a general entropy, representing a suitable information measure for this class. We also show that the group-theoretical structure associated with our multivariate entropies can be used to define a large family of exactly solvable discrete dynamical models. The natural mathematical framework allowing us to formulate this correspondence is offered by the theory of formal groups and rings.