We present an adaptive coupling strategy to induce hysteresis/explosive synchronization in complex networks of phase oscillators (Sakaguchi–Kuramoto model). The coupling strategy ensures explosive synchronization with significant explosive width enhancement. Results show the robustness of the strategy, and the strategy can diminish (by inducing enhanced hysteresis loop) the contrarian impact of phase

A catastrophic bifurcation in non-linear dynamical systems, called crisis, often leads to their convergence to an undesirable non-chaotic state after some initial chaotic transients. Preventing such behavior has been quite challenging. We demonstrate that deep Reinforcement Learning (RL) is able to restore chaos in a transiently chaotic regime of the Lorenz system of equations. Without requiring any

Extreme events appear in many complex nonlinear dynamical systems. Predicting extreme events has important scientific significance and large societal impacts. In this paper, a new mathematical framework of building suitable nonlinear approximate models is developed, which aims at predicting both the observed and hidden extreme events in complex nonlinear dynamical systems for short-, medium-, and long-range

Understanding spatiotemporal patterns of climate extremes has gained considerable relevance in the context of ongoing climate change. With enhanced computational capacity, data driven methods such as functional climate networks have been proposed and have already contributed to significant advances in understanding and predicting extreme events, as well as identifying interrelations between the occurrences

This paper reports a generic method for constructing n-fold covers of 3D conservative chaotic systems, which is derived from the theory of the generalized Hamiltonian system. Three typical example systems are constructed based on the proposed method, and their different n-fold cover chaotic flows are investigated theoretically and numerically. For each example system, the motion trajectories are both

We consider a class of multiplicative processes which, added with stochastic reset events, give origin to stationary distributions with power-law tails—ubiquitous in the statistics of social, economic, and ecological systems. Our main goal is to provide a series of exact results on the dynamics and asymptotic behavior of increasingly complex versions of a basic multiplicative process with resets, including

The brain exhibits intrinsic oscillatory behavior, which plays a vital role in communication and information processing. Abnormalities in brain rhythms have been linked to numerous disorders, including depression and schizophrenia. Rhythmic electrical stimulation (e.g., transcranial magnetic stimulation and transcranial alternating current stimulation) has been used to modulate these oscillations and

The classical concept for emergence of Turing patterns in reaction–diffusion systems requires that a system should be composed of complementary subsystems, one of which is unstable and diffuses sufficiently slowly while the other one is stable and diffuses sufficiently rapidly. In this work, the phenomena of emergence of Turing patterns are studied and do not fit into this concept, yielding the following

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

Crosstalk phenomena taking place between synapses can influence signal transmission and, in some cases, brain functions. It is thus important to discover the dynamic behaviors of the neural network infected by synaptic crosstalk. To achieve this, in this paper, a new circuit is structured to emulate the Coupled Hyperbolic Memristors, which is then utilized to simulate the synaptic crosstalk of a Hopfield

We introduce “state space persistence analysis” for deducing the symbolic dynamics of time series data obtained from high-dimensional chaotic attractors. To this end, we adapt a topological data analysis technique known as persistent homology for the characterization of state space projections of chaotic trajectories and periodic orbits. By comparing the shapes along a chaotic trajectory to those of

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

Acute myocardial ischemia is an imbalance between myocardial blood supply and demand, which is caused by the cessation of blood flow within the heart resulting from an obstruction in one of the major coronary arteries. A severe blockage may result in a region of nonperfused tissue known as ischemic core (IC). As a result, a border zone (BZ) between perfused and nonperfused regions is created due to

In this paper, we introduce an interesting new megastable oscillator with infinite coexisting hidden and self-excited attractors (generated by stable fixed points and unstable ones), which are fixed points and limit cycles stable states. Additionally, by adding a temporally periodic forcing term, we design a new two-dimensional non-autonomous chaotic system with an infinite number of coexisting strange

The synchronization transition in coupled non-smooth systems is studied for increasing coupling strength. The average order parameter is calculated to diagnose synchronization of coupled non-smooth systems. It is found that the coupled non-smooth system exhibits an intermittent synchronization transition from the cluster synchronization state to the complete synchronization state, depending on the

Many systems exhibit both attractive and repulsive types of interactions, which may be dynamic or static. A detailed understanding of the dynamical properties of a system under the influence of dynamically switching attractive or repulsive interactions is of practical significance. However, it can also be effectively modeled with two coexisting competing interactions. In this work, we investigate the

A power packet distribution network is expected to be one of the advanced power distribution systems, providing high controllability in both energy management and failure management. Regarding network operations, the power packet transmission is governed by switching operation within each of the routers. Here, the power distribution through power packets exhibits consensus-like dynamical behaviors

We study the statistics and short-time dynamics of the classical and the quantum Fermi–Pasta–Ulam chain in the thermal equilibrium. We analyze the distributions of single-particle configurations by integrating out the rest of the system. At low temperatures, we observe a systematic increase in the mobility of the chain when transitioning from classical to quantum mechanics due to zero-point energy

Intrinsic predictability is imperative to quantify inherent information contained in a time series and assists in evaluating the performance of different forecasting methods to get the best possible prediction. Model forecasting performance is the measure of the probability of success. Nevertheless, model performance or the model does not provide understanding for improvement in prediction. Intuitively

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

Here, we describe a general-purpose prediction model. Our approach requires three matrices of equal size and uses two equations to determine the behavior against two possible outcomes. We use an example based on photon-pixel coupling data to show that in humans, this solution can indicate the predisposition to disease. An implementation of this model is made available in the supplementary material

The objective of this study is to examine the multi-scale feature of volatility spillover in the energy stock market systematically. To achieve this objective, a framework is proposed. First, the wavelet theory is used to divide the original data to subsequences to analyze the multi-scale features, and then the Generalized Autoregressive Conditional Heteroskedasticity model with Baba, Engle, Kraft

Some physical systems with interacting chaotic subunits, when synchronized, exhibit a dynamical transition from chaos to limit cycle oscillations via intermittency such as during the onset of oscillatory instabilities that occur due to feedback between various subsystems in turbulent flows. We depict such a transition from chaos to limit cycle oscillations via intermittency when a grid of chaotic oscillators

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

Inverse stochastic resonance comprises a nonlinear response of an oscillatory system to noise where the frequency of noise-perturbed oscillations becomes minimal at an intermediate noise level. We demonstrate two generic scenarios for inverse stochastic resonance by considering a paradigmatic model of two adaptively coupled stochastic active rotators whose local dynamics is close to a bifurcation threshold

Global organization of three-dimensional (3D) Lagrangian chaotic transport is difficult to infer without extensive computation. For 3D time-periodic flows with one invariant, we show how constraints on deformation that arise from volume-preservation and periodic lines result in resonant degenerate points that periodically have zero net deformation. These points organize all Lagrangian transport in

We numerically study a network of two identical populations of identical real-valued quadratic maps. Upon variation of the coupling strengths within and across populations, the network exhibits a rich variety of distinct dynamics. The maps in individual populations can be synchronized or desynchronized. Their temporal evolution can be periodic or aperiodic. Furthermore, one can find blends of synchronized

We present the use of modern machine learning approaches to suppress self-sustained collective oscillations typically signaled by ensembles of degenerative neurons in the brain. The proposed hybrid model relies on two major components: an environment of oscillators and a policy-based reinforcement learning block. We report a model-agnostic synchrony control based on proximal policy optimization and

Because the collapse of complex systems can have severe consequences, vulnerability is often seen as the core problem of complex systems. Multilayer networks are powerful tools to analyze complex systems, but complex networks may not be the best choice to mimic subsystems. In this work, a cellular graph (CG) model is proposed within the framework of multilayer networks to analyze the vulnerability

We show how to couple phase-oscillators on a graph so that collective dynamics “searches” for the coloring of that graph as it relaxes toward the dynamical equilibrium. This translates a combinatorial optimization problem (graph coloring) into a functional optimization problem (finding and evaluating the global minimum of dynamical non-equilibrium potential, done by the natural system’s evolution)

The research of finding hidden attractors in nonlinear dynamical systems has attracted much consideration because of its practical and theoretical importance. A new fractional order four-dimensional system, which can exhibit some hidden hyperchaotic attractors, is proposed in this paper. The predictor–corrector method of the Adams–Bashforth–Moulton algorithm and the parameter switching algorithm are

Permutation Entropy (PE) is a cost effective tool for summarizing the complexity of a time series. It has been used in many applications including damage detection, disease forecasting, detection of dynamical changes, and financial volatility analysis. However, to successfully use PE, an accurate selection of two parameters is needed: the permutation dimension n and embedding delay τ. These parameters

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

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

We study localized patterns in an exact mean-field description of a spatially extended network of quadratic integrate-and-fire neurons. We investigate conditions for the existence and stability of localized solutions, so-called bumps, and give an analytic estimate for the parameter range, where these solutions exist in parameter space, when one or more microscopic network parameters are varied. We

In this paper, almost sure exponential stabilization and destabilization criteria for nonlinear systems are obtained via aperiodically intermittent stochastic noises based on average techniques and piecewise continuous scalar functions. Compared with existing results on almost sure exponential stability of stochastic systems, the requirement on the upper bound of the diffusion operator of a Lyapunov

The present paper concerns a new description of changing in metabolism during incremental exercises test that permit an individually tailored program of exercises for obese subjects. We analyzed heart rate variability from RR interval time series (tachogram) with an alternative approach, the recurrence quantification analysis, that allows a description of a time series in terms of its dynamic structure

The logistic map, whose iterations lead to period doubling and chaos as the control parameter, is increased and has three cases of the control parameter where exact solutions are known. In this paper, we show that general solutions also exist for other values of the control parameter. These solutions employ a special function, not expressible in terms of known analytical functions. A method of calculating

We analyze fractional Sturm–Liouville problems with a new generalized fractional derivative in five different forms. We investigate the representation of solutions by means of ρ-Laplace transform for generalized fractional Sturm–Liouville initial value problems. Finally, we examine eigenfunctions and eigenvalues for generalized fractional Sturm–Liouville boundary value problems. All results obtained

Power systems are subject to fundamental changes due to the increasing infeed of decentralized renewable energy sources and storage. The decentralized nature of the new actors in the system requires new concepts for structuring the power grid and achieving a wide range of control tasks ranging from seconds to days. Here, we introduce a multiplex dynamical network model covering all control timescales

Whether listening to overlapping conversations in a crowded room or recording the simultaneous electrical activity of millions of neurons, the natural world abounds with sparse measurements of complex overlapping signals that arise from dynamical processes. While tools that separate mixed signals into linear sources have proven necessary and useful, the underlying equational forms of most natural signals

In this paper, the effects of asymmetry in an electrical synaptic connection between two neuronal oscillators with a small discrepancy are studied in a 2D Hindmarsh-Rose model. We have found that the introduced model possesses a unique unstable equilibrium point. We equally demonstrate that the asymmetric electrical couplings as well as external stimulus induce the coexistence of bifurcations and multiple

We propose a novel type of neural networks known as "attention-based sequence-to-sequence architecture" for a model-free prediction of spatiotemporal systems. This architecture is composed of an encoder and a decoder in which the encoder acts upon a given input sequence and then the decoder yields another output sequence to make a multistep prediction at a time. In order to demonstrate the potential

We study the totally asymmetric simple exclusion process on multiplex networks, which consist of a fixed set of vertices (junctions) connected by different types of links (segments). In particular, we assume that there are two types of segments corresponding to two different values of hopping rate of particles (larger hopping rate indicates particles move with higher speed on the segments). By simple

An important task in the post-gene era is to understand the role of stochasticity in gene regulation. Here, we analyze a cascade model of stochastic gene expression, where the upstream gene stochastically generates proteins that regulate, as transcription factors, stochastic synthesis of the downstream output. We find that in contrast to fast input fluctuations that do not change the behavior of the

We propose a simple mathematical model that describes the time evolution of a self-propelled object on a liquid surface using variables such as object location, surface concentration of active molecules, and hydrodynamic surface flow. The model is applied to simulate the time evolution of a rotor composed of a polygonal plate with camphor pills at its corners. We have qualitatively reproduced results

This work investigates the time response of a Duffing oscillator with time-varying parameters (excitation frequency, linear stiffness, and mass) by approximate analytical and numerical methods. When the excitation frequency sweep covers the multisolution range, the characteristics of the response (maximum response, jump-up frequency, and jump-down frequency) mainly depend on the frequency sweep rate

Open quantum systems can exhibit complex states, for which classification and quantification are still not well resolved. The Kerr-nonlinear cavity, periodically modulated in time by coherent pumping of the intracavity photonic mode, is one of the examples. Unraveling the corresponding Markovian master equation into an ensemble of quantum trajectories and employing the recently proposed calculation

Here, we investigate the sensitivity of nonequilibrium Casimir forces to optical properties at low frequencies via the Drude and plasma models and the associated effects on the actuation of microelectromechanical systems. The stability and chaotic motion for both autonomous conservative and nonconservative driven systems were explored assuming good, e.g., Au, and poor, e.g., doped SiC, interacting

Investigation on linear/nonlinear resonance phenomena and supercritical/subcritical pitchfork bifurcation mechanism is reported in a complex bifractional-order damped system which endures a high-frequency parametric excitation and contains fractional-power nonlinearity. The approximate theoretical expression of the linear response amplitude at the primary frequency and the superharmonic response amplitude

Low-emissions can-annular gas turbines are prone to develop low-frequency self-excited thermoacoustic oscillations. Such oscillations arise from the coupling between adjacent combustors and can increase wear and thermal stresses. In this experimental study, we explore the mutual synchronization of two thermoacoustic oscillators (i.e., two model combustors) interacting via dissipative and time-delayed

The development of new approaches to detect motor-related brain activity is key in many aspects of science, especially in brain-computer interface applications. Even though some well-known features of motor-related electroencephalograms have been revealed using traditionally applied methods, they still lack a robust classification of motor-related patterns. Here, we introduce new features of motor-related

The framework of statistical inference has been successfully used to detect the mesoscale structures in complex networks such as community structure and core-periphery (CP) structure. The main principle is that the stochastic block model is used to fit the observed network and the learned parameters indicating the group assignment, in which the parameters of model are often calculated via an expectation-maximization

We consider the linear and quadratic higher-order terms associated with the response of the statistical properties of a dynamical system to suitable small perturbations. These terms are related to the first and second derivative of the stationary measure with respect to the changes in the system itself, expressing how the statistical properties of the system vary under the perturbation. We show a general

It is a challenging problem to assign communities in a complex network so that nodes in a community are tightly connected on the basis of higher-order connectivity patterns such as motifs. In this paper, we develop an efficient algorithm that detects communities based on higher-order structures. Our algorithm can also detect communities based on a signed motif, a colored motif, a weighted motif, as

Measures of centrality in networks defined by means of matrix algebra, like PageRank-type centralities, have been used for over 70 years. Recently, new extensions of PageRank have been formulated and may include a personalization (or teleportation) vector. It is accepted that one of the key issues for any centrality measure formulation is to what extent someone can control its variability. In this

As the potential for a treatment of Duchenne muscular dystrophy (DMD) grows, the need for methods for the early diagnosis of DMD becomes more and more important. Clinical experiences suggest that children with DMD will show some lack of motor ability in the early stage when compared with children at the same age, especially in balance and coordination abilities. Is it possible to quantify the coordination

In this paper, we examine the deviations from Gaussianity for two types of a random variable converging to a normal distribution, namely, sums of random variables generated by a deterministic discrete time map and a linearly damped variable driven by a deterministic map. We demonstrate how Edgeworth expansions provide a universal description of the deviations from the limiting normal distribution.

Steiner's circumellipse is the unique geometric regularization of any triangle to a circumscribed ellipse with the same centroid, a regularization that motivates our introduction of the Steiner triangle as a minimal model for liquid droplet dynamics. The Steiner drop is a deforming triangle with one side making sliding contact against a planar basal support. The center of mass of the triangle is governed

A set-reset latch is a basic building block of computers and can be used to store state information. Here, by testing the influence of the two logical input signals on the reliable set-reset latch logic operation in the bistable system, we found that there are two types of input signals, namely, suprathreshold and subthreshold signals. For the suprathreshold signals, reliable set-reset logic operation