Furthermore, the influence of the source motion on the RBD algorithm is quantified both numerically and experimentally.This paper investigates the exponential bipartite synchronization of a general class of delayed signed networks with multi-links by using an aperiodically intermittent control strategy. The main result is a set of sufficient conditions for bipartite synchronization that depend on the network's topology, control gain, and the maximum proportion of rest time. An application to Chua's circuits is then considered, and some numerical simulation results are presented.Quantifying respiratory sinus arrhythmia (RSA) can provide an index of parasympathetic function. Fourier spectral analysis, the most widely used approach, estimates the power of the heart rate variability in the frequency band of breathing. However, it neglects the time-varying characteristics of the transitions as well as the nonlinear properties of the cardio-respiratory coupling. Here, we propose a novel approach based on Hilbert-Huang transform, called the multimodal coupling analysis (MMCA) method, to assess cardio-respiratory dynamics by examining the instantaneous nonlinear phase interactions between two interconnected signals (i.e., heart rate and respiration) and compare with the counterparts derived from the wavelet-based method. We used an online database. ABT-199 Bcl-2 inhibitor The corresponding RSA components of the 90-min ECG and respiratory signals of 20 young and 20 elderly healthy subjects were extracted and quantified. A cycle-based analysis and a synchro-squeezed wavelet transform were also introduced to assess the amplitude or phase changes of each respiratory cycle. Our results demonstrated that the diminished mean and standard deviation of the derived dynamical RSA activities can better discriminate between elderly and young subjects. Moreover, the degree of nonlinearity of the cycle-by-cycle RSA waveform derived from the differences between the instantaneous frequency and the mean frequency of each respiratory cycle was significantly decreased in the elderly subjects by the MMCA method. The MMCA method in combination with the cycle-based analysis can potentially be a useful tool to depict the aging changes of the parasympathetic function as well as the waveform nonlinearity of RSA compared to the Fourier-based high-frequency power and the wavelet-based method.In this paper, we provide a numerical tool to study a material's coherence from a set of 2D Lagrangian trajectories sampling a dynamical system, i.e., from the motion of passive tracers. We show that eigenvectors of the Burau representation of a topological braid derived from the trajectories have levelsets corresponding to components of the Nielsen-Thurston decomposition of the dynamical system. One can thus detect and identify clusters of space-time trajectories corresponding to coherent regions of the dynamical system by solving an eigenvalue problem. Unlike previous methods, the scalable computational complexity of our braid-based approach allows the analysis of large amounts of trajectories.The dynamics of cardiac fibrillation can be described by the number, the trajectory, the stability, and the lifespan of phase singularities (PSs). Accurate PS tracking is straightforward in simple uniform tissues but becomes more challenging as fibrosis, structural heterogeneity, and strong anisotropy are combined. In this paper, we derive a mathematical formulation for PS tracking in two-dimensional reaction-diffusion models. The method simultaneously tracks wavefronts and PS based on activation maps at full spatiotemporal resolution. PS tracking is formulated as a linear assignment problem solved by the Hungarian algorithm. The cost matrix incorporates information about distances between PS, chirality, and wavefronts. A graph of PS trajectories is generated to represent the creations and annihilations of PS pairs. Structure-preserving graph transformations are applied to provide a simplified description at longer observation time scales. The approach is validated in 180 simulations of fibrillation in four different types of substrates featuring, respectively, wavebreaks, ionic heterogeneities, fibrosis, and breakthrough patterns. The time step of PS tracking is studied in the range from 0.1 to 10 ms. The results show the benefits of improving time resolution from 1 to 0.1 ms. The tracking error rate decreases by an order of magnitude because the occurrence of simultaneous events becomes less likely. As observed on PS survival curves, the graph-based analysis facilitates the identification of macroscopically stable rotors despite wavefront fragmentation by fibrosis.Recently, the coexistence of initial-boosting attractors in continuous-time systems has been attracting more attention. How do you implement the coexistence of initial-boosting attractors in a discrete-time map? To address this issue, this paper proposes a novel two-dimensional (2D) hyperchaotic map with a simple algebraic structure. The 2D hyperchaotic map has two special cases of line and no fixed points. The parameter-dependent and initial-boosting bifurcations for these two cases of line and no fixed points are investigated by employing several numerical methods. The simulated results indicate that complex dynamical behaviors including hyperchaos, chaos, and period are closely related to the control parameter and initial conditions. Particularly, the boosting bifurcations of the 2D hyperchaotic map are switched by one of its initial conditions. The distinct property allows the dynamic amplitudes of hyperchaotic/chaotic sequences to be controlled by switching the initial condition, which is especially suitable for chaos-based engineering applications. Besides, a microcontroller-based hardware platform is developed to confirm the generation of initial-switched boosting hyperchaos/chaos.Global climate change affects marine species including phytoplankton, which constitute the base of the marine food web, by changing the primary productivity. Global warming affects the ocean surface temperature, in turn leading to a change in the oxygen production of phytoplankton. In this work, the fractional oxygen-phytoplankton-zooplankton mathematical model is considered by the Caputo fractional operator. The production rate of photosynthesis is determined by a temperature function. The model is, therefore, based on the idea that the rate of photosynthesis changes due to the impact of global warming, while phytoplankton oxygen production increases and decreases. We analyze the model with the Caputo fractional derivative differently from the classical case of the model and we compare the results with the integer order derivative when α tends to 1. Existence and uniqueness properties of the oxygen-plankton model have been proved by means of a local Lipschitz condition. It was shown that the species are more sustainable than its corresponding classical case in the Caputo model.