Chaos

Article	Citations
On explaining the surprising success of reservoir computing forecaster of chaos? The universal machine learning dynamical system with contrast to VAR and DMD	91
Synchronization in Hindmarsh–Rose neurons subject to higher-order interactions	90
Multi-scroll hidden attractor in memristive HR neuron model under electromagnetic radiation and its applications	87
COVID-19 second wave mortality in Europe and the United States	82
FitzHugh–Nagumo oscillators on complex networks mimic epileptic-seizure-related synchronization phenomena	77
Stiff neural ordinary differential equations	68
A memristive neuron and its adaptability to external electric field	60
Modeling the second wave of COVID-19 infections in France and Italy via a stochastic SEIR model	57
Dynamics of a fractional epidemiological model with disease infection in both the populations	48
Intralayer and interlayer synchronization in multiplex network with higher-order interactions	46
High-dimensional nonlinear wave transitions and their mechanisms	45
Memristor-type chaotic mapping	44
Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate,regime transitions, and the effect of stochasticity	43
Fractional SEIR model and data-driven predictions of COVID-19 dynamics of Omicron variant	42
Simplicial SIRS epidemic models with nonlinear incidence rates	41
Do reservoir computers work best at the edge of chaos?	41
Complex dynamics in a Hopfield neural network under electromagnetic induction and electromagnetic radiation	39
Fractional-calculus analysis of the transmission dynamics of the dengue infection	38
The stochastic bifurcation analysis and stochastic delayed optimal control for epidemic model with general incidence function	38
ordpy: A Python package for data analysis with permutation entropy and ordinal network methods	37
Resonance and bifurcation of fractional quintic Mathieu–Duffing system	37
Rogue waves for the fourth-order nonlinear Schrödinger equation on the periodic background	35
Caputo–Hadamard fractional differential equations on time scales: Numerical scheme, asymptotic stability, and chaos	34
Mathematical modeling of COVID-19: Impact of non-pharmaceutical interventions in India	34
Effects of temperature and ion channel blocks on propagation of action potential in myelinated axons	34

Complex nonlinear dynamics and vibration suppression of conceptual airfoil models: A state-of-the-art overview	33
Integrated information as a common signature of dynamical and information-processing complexity	33
Neuron-like spiking and bursting in Josephson junctions: A review	31
Collective behavior in a two-layer neuronal network with time-varying chemical connections that are controlled by a Petri net	30
A 2D hyperchaotic map with conditional symmetry and attractor growth	30
Reduced-order models for coupled dynamical systems: Data-driven methods and the Koopman operator	30
Offset parameter cancellation produces countless coexisting attractors	29
Physics-informed neural networks and functional interpolation for stiff chemical kinetics	29
Postural instability via a loss of intermittent control in elderly and patients with Parkinson’s disease: A model-based and data-driven approach	29
Exploring dynamical complexity in a time-delayed tumor-immune model	29
Homoclinic chaos in the Rössler model	28
Using data assimilation to train a hybrid forecast system that combines machine-learning and knowledge-based components	27
Interplay of simplicial awareness contagion and epidemic spreading on time-varying multiplex networks	27
Effect of rate of change of parameter on early warning signals for critical transitions	27
Fractional q-deformed chaotic maps: A weight function approach	27
Efficiency of communities and financial markets during the 2020 pandemic	27
Consensus on simplicial complexes: Results on stability and synchronization	26
Deep learning enhanced dynamic mode decomposition	26
Betweenness centrality of teams in social networks	25
Transition paths of marine debris and the stability of the garbage patches	25
Collective steady-state patterns of swarmalators with finite-cutoff interaction distance	25
Enhanced logical chaotic resonance	25
Coexistence of infinitely many patterns and their control in heterogeneous coupled neurons through a multistable memristive synapse	24
Reservoir computing as digital twins for nonlinear dynamical systems	24
Early detection of thermoacoustic instabilities in a cryogenic rocket thrust chamber using combustion noise features and machine learning	24
Many-body quantum chaos and dual-unitarity round-a-face	24
Scenarios of hyperchaos occurrence in 4D Rössler system	23
Sliding homoclinic bifurcations in a Lorenz-type system: Analytic proofs	23
Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing	23
Effect of magnetic induction on the synchronizability of coupled neuron network	23
Homological percolation transitions in growing simplicial complexes	23
Effortless estimation of basins of attraction	23
Hidden coexisting firings in fractional-order hyperchaotic memristor-coupled HR neural network with two heterogeneous neurons and its applications	23
Breaking symmetries of the reservoir equations in echo state networks	23
Extreme synchronization events in a Kuramoto model: The interplay between resource constraints and explosive transitions	23
Detecting the maximum likelihood transition path from data of stochastic dynamical systems	22
Measuring synchrony in bio-medical timeseries	22
Mitigating long transient time in deterministic systems by resetting	22
Targeting attack hypergraph networks	22
Translational approaches to treating dynamical diseases through in silico clinical trials	22
Evolutionary multigame with conformists and profiteers based on dynamic complex networks	22
Effect of local and global information on the dynamical interplay between awareness and epidemic transmission in multiplex networks	22
Noise induced suppression of spiral waves in a hybrid FitzHugh–Nagumo neuron with discontinuous resetting	22
The Kuramoto model on a sphere: Explaining its low-dimensional dynamics with group theory and hyperbolic geometry	21
Repulsive inter-layer coupling induces anti-phase synchronization	21
Routes toward chaos in a memristor-based Shinriki circuit	21
Data-driven reduced-order modeling of spatiotemporal chaos with neural ordinary differential equations	21
Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions	21
Neuronal synchronization in long-range time-varying networks	21
Design of a fractional-order atmospheric model via a class of ACT-like chaotic system and its sliding mode chaos control	21

Generalized multistability and its control in a laser	21
Balanced Hodge Laplacians optimize consensus dynamics over simplicial complexes	20
Convolutional neural networks predict the onset of paroxysmal atrial fibrillation: Theory and applications	20
Optimizing memory in reservoir computers	20
An eco-epidemiological model with the impact of fear	20
Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology	20
Coherent oscillations in balanced neural networks driven by endogenous fluctuations	20
Traveling of extreme events in network of counter-rotating nonlinear oscillators	20
Multistability analysis and nonlinear vibration for generator set in series hybrid electric vehicle through electromechanical coupling	20
Quint points lattice in a driven Belousov–Zhabotinsky reaction model	20
Optimized ensemble deep learning framework for scalable forecasting of dynamics containing extreme events	20
Nonlinear dynamics of a single-gap terahertz split-ring resonator under electromagnetic radiation	20
Global analysis of stochastic bifurcation in shape memory alloy supporter with the extended composite cell coordinate system method	19
Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations	19
Physical approach of a neuron model with memristive membranes	19
Some new and modified fractional analysis of the time-fractional Drinfeld–Sokolov–Wilson system	19
On discrete Lorenz-like attractors	19
Learning spatiotemporal chaos using next-generation reservoir computing	19
Amplitude-modulated spiking as a novel route to bursting: Coupling-induced mixed-mode oscillations by symmetry breaking	19
Perspectives on adaptive dynamical systems	19
Coupled spreading between information and epidemics on multiplex networks with simplicial complexes	19
Bifurcations, chaos, and multistability in a nonautonomous predator–prey model with fear	19
Observers-based event-triggered adaptive fuzzy backstepping synchronization of uncertain fractional order chaotic systems	19
Controlling species densities in structurally perturbed intransitive cycles with higher-order interactions	19
Vital node identification in hypergraphs via gravity model	19
A novel non-equilibrium memristor-based system with multi-wing attractors and multiple transient transitions	18
Replicator dynamics of public goods games with global exclusion	18
Using machine learning to anticipate tipping points and extrapolate to post-tipping dynamics of non-stationary dynamical systems	18
Spontaneous symmetry breaking and ghost states supported by the fractional PT-symmetric saturable nonlinear Schrödinger equation	18
Spectral analysis of the Koopman operator for partial differential equations	18
Robust forecasting using predictive generalized synchronization in reservoir computing	18
Identifying influential nodes: A new method based on network efficiency of edge weight updating	18
Bifurcation, chaos, multistability, and organized structures in a predator–prey model with vigilance	18
Impact of fear effect and prey refuge on a fractional order prey–predator system with Beddington–DeAngelis functional response	18
Random-matrix theory for the Lindblad master equation	18
Four-wave mixing and coherently coupled Schrödinger equations: Cascading processes and Fermi–Pasta–Ulam–Tsingou recurrence	18
On the averaging principle for stochastic differential equations involving Caputo fractional derivative	18
Accuracy of neural networks for the simulation of chaotic dynamics: Precision of training data vs precision of the algorithm	18
Nonlinear dynamical behavior of an SEIR mathematical model: Effect of information and saturated treatment	18
Bistability in a tri-trophic food chain model: Basin stability perspective	18
Spatial evolution of cooperation with variable payoffs	17
Synchronization in the Kuramoto model in presence of stochastic resetting	17
Dynamics study on the effect of memristive autapse distribution on Hopfield neural network	17
Unbalanced clustering and solitary states in coupled excitable systems	17
Explosive synchronization in interlayer phase-shifted Kuramoto oscillators on multiplex networks	17
Predicting critical transitions in multiscale dynamical systems using reservoir computing	17
Shilnikov attractors in three-dimensional orientation-reversing maps	17
Transient dynamics and multistability in two electrically interacting FitzHugh–Nagumo neurons	17
Noise-driven multistability vs deterministic chaos in phenomenological semi-empirical models of whole-brain activity	17
Automatic detection of abrupt transitions in paleoclimate records	17
A novel four-step feedback procedure for rapid control of chaotic behavior of the logistic map and unstable traffic on the road	17
Generalized splay states in phase oscillator networks	17
A phytoplankton–zooplankton–fish model with chaos control: In the presence of fear effect and an additional food	17
Diffusion-induced regular and chaotic patterns in a ratio-dependent predator–prey model with fear factor and prey refuge	17
Quantum hydrodynamic theory of quantum fluctuations in dipolar Bose–Einstein condensate	17
Dynamical analysis of monkeypox transmission incorporating optimal vaccination and treatment with cost-effectiveness	17
A reliable chaos-based cryptography using Galois field	17
Model-free prediction of multistability using echo state network	17
The impact of non-pharmaceutical interventions on the prevention and control of COVID-19 in New York City	16
Optimal flatness placement of sensors and actuators for controlling chaotic systems	16
Fractional calculus with exponential memory	16
Cluster synchronization of networks via a canonical transformation for simultaneous block diagonalization of matrices	16
A generalized permutation entropy for noisy dynamics and random processes	16
Revealing a multiplex brain network through the analysis of recurrences	16
Two-dimensional memristive hyperchaotic maps with different coupling frames and its hardware implementation	16
A complex network approach to study the extreme precipitation patterns in a river basin	16
Characteristics of 2020 stock market crash: The COVID-19 induced extreme event	16
Symmetry breaking of solitons in the PT-symmetric nonlinear Schrödinger equation with the cubic–quintic competing saturable nonlinearity	16
An overview of epidemic models with phase transitions to absorbing states running on top of complex networks	16
Melnikov-type method for a class of planar hybrid piecewise-smooth systems with impulsive effect and noise excitation: Heteroclinic orbits	16
Parity-time-symmetric rational vector rogue waves of the n-component nonlinear Schrödinger equation	16
Knowledge-based learning of nonlinear dynamics and chaos	16
Optimal test-kit-based intervention strategy of epidemic spreading in heterogeneous complex networks	16
Finding nonlinear system equations and complex network structures from data: A sparse optimization approach	16
Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning	16
The impact of nodes of information dissemination on epidemic spreading in dynamic multiplex networks	16
Rate-dependent tipping and early warning in a thermoacoustic system under extreme operating environment	15
Fractional Brownian motion with random Hurst exponent: Accelerating diffusion and persistence transitions	15
Low-carbon technology collaborative innovation in industrial cluster with social exclusion: An evolutionary game theory perspective	15
Revealing spatiotemporal interaction patterns behind complex cities	15

Probabilistic response of a fractional-order hybrid vibration energy harvester driven by random excitation	15
Multifractal detrended cross-correlation analysis of wind speed and solar radiation	15
Multifunctionality in a reservoir computer	15
Dynamics of fractional N-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schrödinger equations	15
Locally active memristor based oscillators: The dynamic route from period to chaos and hyperchaos	15
Learn to synchronize, synchronize to learn	15
Stochastic switches of eutrophication and oligotrophication: Modeling extreme weather via non-Gaussian Lévy noise	15
On infinite homoclinic orbits induced by unstable periodic orbits in the Lorenz system	15
Characterizing dynamical transitions by statistical complexity measures based on ordinal pattern transition networks	15
A hyperchaotic cycloid map with attractor topology sensitive to system parameters	15
Existence and controllability for conformable fractional stochastic differential equations with infinite delay via measures of noncompactness	15
Control of tipping points in stochastic mutualistic complex networks	14
Chaos in the peroxidase–oxidase oscillator	14
Noise-induced stabilization of the FitzHugh–Nagumo neuron dynamics: Multistability and transient chaos	14
Averaging principle for stochastic differential equations under a weak condition	14
Averaging principle for a type of Caputo fractional stochastic differential equations	14
Boundary dynamics of a non-smooth memristive Hindmarsh–Rose neuron system	14
Bifurcations of mixed-mode oscillations in three-timescale systems: An extended prototypical example	14
Degenerated Liouvillians and steady-state reduced density matrices	14
Structural anomalies in brain networks induce dynamical pacemaker effects	14
Transition to hyperchaos: Sudden expansion of attractor and intermittent large-amplitude events in dynamical systems	14
An end-to-end deep learning approach for extracting stochastic dynamical systems with α -stable Lévy noise	14
Classification of fold/hom and fold/Hopf spike-adding phenomena	14
Fast optimal entrainment of limit-cycle oscillators by strong periodic inputs via phase-amplitude reduction and Floquet theory	14
Analysis of inter-transaction time fluctuations in the cryptocurrency market	14
Synchronization in cilia carpets and the Kuramoto model with local coupling: Breakup of global synchronization in the presence of noise	14
Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks	14
Quasi-objective coherent structure diagnostics from single trajectories	14
Basic fractional nonlinear-wave models and solitons	14
Nonlinear excitations of magnetosonic solitary waves and their chaotic behavior in spin-polarized degenerate quantum magnetoplasma	14
Persistence in multilayer ecological network consisting of harvested patches	13
Stochastic analysis of COVID-19 by a SEIR model with Lévy noise	13
Causality indices for bivariate time series data: A comparative review of performance	13
Machine learning evaluates changes in functional connectivity under a prolonged cognitive load	13
Wavelet skeletons in sleep EEG-monitoring as biomarkers of early diagnostics of mild cognitive impairment	13
Noisy consensus dynamics in windmill-type graphs	13
Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave–particle entity	13
Rapid frontal polymerization achieved with thermally conductive metal strips	13
Theory of quasi-simple dispersive shock waves and number of solitons evolved from a nonlinear pulse	13
Effect of time delay in a bistable synthetic gene network	13
Controlling the spontaneous firing behavior of a neuron with astrocyte	13
Mixed-mode oscillations from a constrained extended Bonhoeffer–van der Pol oscillator with a diode	13
Synchronization of clocks and metronomes: A perturbation analysis based on multiple timescales	13
Wave-packet behaviors of the defocusing nonlinear Schrödinger equation based on the modified physics-informed neural networks	13
Some elements for a history of the dynamical systems theory	13
Asymmetric adaptivity induces recurrent synchronization in complex networks	13
In search of peak human athletic potential: A mathematical investigation	13
Diffuse reflectance and machine learning techniques to differentiate colorectal cancer ex vivo	13
Interrupting vaccination policies can greatly spread SARS-CoV-2 and enhance mortality from COVID-19 disease: The AstraZeneca case for France and Italy	13
Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling	13
Network spreading among areas: A dynamical complex network modeling approach	12
Offset boosting in a discrete system	12
Nonlinear model reduction to fractional and mixed-mode spectral submanifolds	12
Model selection of chaotic systems from data with hidden variables using sparse data assimilation	12
Symmetrical Hopf-induced bursting and hyperchaos control in memristor-based circuit	12
Agent-based modeling: Population limits and large timescales	12
Chaos–hyperchaos transition in three identical quorum-sensing mean-field coupled ring oscillators	12
Stability analysis of multiplayer games on adaptive simplicial complexes	12
Asymmetrical dynamics of epidemic propagation and awareness diffusion in multiplex networks	12
Neuronal synchronization in time-varying higher-order networks	12
Phase-field-crystal description of active crystallites: Elastic and inelastic collisions	12
Toward interpretability of machine learning methods for the classification of patients with major depressive disorder based on functional network measures	12
Game dynamics of emotion evolution based on the Moran process	12
Active learning and relevance vector machine in efficient estimate of basin stability for large-scale dynamic networks	12
Two competing simplicial irreversible epidemics on simplicial complex	12
Dynamics of the threshold model on hypergraphs	12
Solitary states in the mean-field limit	12
Learning unseen coexisting attractors	12
Hypergraph assortativity: A dynamical systems perspective	12
Symplectic Gaussian process regression of maps in Hamiltonian systems	12
Early-warning signals for disease activity in patients diagnosed with multiple sclerosis based on keystroke dynamics	12
Site percolation thresholds on triangular lattice with complex neighborhoods	12
Maximally predictive states: From partial observations to long timescales	12
Optimal time-varying coupling function can enhance synchronization in complex networks	12
Predicting attractor characteristics using Lyapunov exponents in a laser with injected signal	12
Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators	12
Revival of oscillation and symmetry breaking in coupled quantum oscillators	12
Dynamics of advectively coupled Van der Pol equations chain	12
Noise-driven topological changes in chaotic dynamics	12
Disintegrating spatial networks based on region centrality	12
Condensation in the phase space and network topology during transition from chaos to order in turbulent thermoacoustic systems	12
Reversible chemical reactions model with fractional difference operator: Dynamical analysis and synchronization	12
Synchronization of discrete fractional-order complex networks with and without unknown topology	12
Synchronization of phase oscillators on complex hypergraphs	12
Sequential seeding in multilayer networks	12
Discrimination of sunflower seeds using multispectral and texture dataset in combination with region selection and supervised classification methods	12
Time shifts to reduce the size of reservoir computers	12
On the interpretation of Dirac δ pulses in differential equations for phase oscillators	11
Optimal control of the reaction–diffusion process on directed networks	11
Dual-domain analysis of gun violence incidents in the United States	11
The 16th Hilbert problem for discontinuous piecewise isochronous centers of degree one or two separated by a straight line	11
Impact of simplicial complexes on epidemic spreading in partially mapping activity-driven multiplex networks	11
Noise-induced complex oscillatory dynamics in the Zeldovich–Semenov model of a continuous stirred tank reactor	11
Synchronization of wave structures in a heterogeneous multiplex network of 2D lattices with attractive and repulsive intra-layer coupling	11
Multiscale measures of phase-space trajectories	11