Nonlinear Dynamics

Article	Citations
SEIR modeling of the COVID-19 and its dynamics	437
Designs, analysis, and applications of nonlinear energy sinks	232
Interaction solutions to nonlinear partial differential equations via Hirota bilinear forms: one-lump-multi-stripe and one-lump-multi-soliton types	216
Bäcklund transformation, exact solutions and diverse interaction phenomena to a (3+1)-dimensional nonlinear evolution equation	153
Data-driven femtosecond optical soliton excitations and parameters discovery of the high-order NLSE using the PINN	150
Firing multistability in a locally active memristive neuron model	145
New extended Kadomtsev–Petviashvili equation: multiple soliton solutions, breather, lump and interaction solutions	144
Rogue wave solutions and the bright and dark solitons of the (3+1)-dimensional Jimbo–Miwa equation	133
Color image encryption using orthogonal Latin squares and a new 2D chaotic system	133
Nonlinear forced vibration of functionally graded graphene platelet-reinforced metal foam cylindrical shells: internal resonances	130
Review on chaotic dynamics of memristive neuron and neural network	128
A fast and efficient multiple images encryption based on single-channel encryption and chaotic system	128
Bilinear residual network method for solving the exactly explicit solutions of nonlinear evolution equations	126
Initial offset boosting coexisting attractors in memristive multi-double-scroll Hopfield neural network	125
Coupled spatial periodic waves and solitons in the photovoltaic photorefractive crystals	121
Generalized logistic growth modeling of the COVID-19 outbreak: comparing the dynamics in the 29 provinces in China and in the rest of the world	119
A fractional-order model for the novel coronavirus (COVID-19) outbreak	117
Stability and optimal control strategies for a novel epidemic model of COVID-19	114
Transmission dynamics of COVID-19 in Wuhan, China: effects of lockdown and medical resources	114
A novel simple chaotic circuit based on memristor–memcapacitor	113
Nonlinear forced vibrations of FGM sandwich cylindrical shells with porosities on an elastic substrate	113
Robust fixed-time attitude stabilization control of flexible spacecraft with actuator uncertainty	110
Input-to-state stability of impulsive reaction–diffusion neural networks with infinite distributed delays	109
Managements of scalar and vector rogue waves in a partially nonlocal nonlinear medium with linear and harmonic potentials	102
Painlevé analysis, auto-Bäcklund transformation and analytic solutions of a (2$$+$$1)-dimensional generalized Burgers system with the variable coefficients in a fluid	100

A nonlinear vibration isolator supported on a flexible plate: analysis and experiment	98
Dynamical analysis of a new chaotic system: asymmetric multistability, offset boosting control and circuit realization	98
Chaos cloud quantum bat hybrid optimization algorithm	97
Parameter estimation of the incubation period of COVID-19 based on the doubly interval-censored data model	96
Design and application of an S-box using complete Latin square	92
Bright soliton solutions of the (2+1)-dimensional generalized coupled nonlinear Schrödinger equation with the four-wave mixing term	91
Coexisting firing patterns and phase synchronization in locally active memristor coupled neurons with HR and FN models	90
Soliton interaction control through dispersion and nonlinear effects for the fifth-order nonlinear Schrödinger equation	89
Prediction and dynamical evolution of multipole soliton families in fractional Schrödinger equation with the PT-symmetric potential and saturable nonlinearity	87
A nonlinear ultra-low-frequency vibration isolator with dual quasi-zero-stiffness mechanism	85
An image encryption scheme based on multi-objective optimization and block compressed sensing	85
Bilinear form, soliton, breather, lump and hybrid solutions for a ($$\varvec{2+1}$$)-dimensional Sawada–Kotera equation	84
Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: application to COVID-19 pandemic	84
Short memory fractional differential equations for new memristor and neural network design	83
Robust identification for fault detection in the presence of non-Gaussian noises: application to hydraulic servo drives	81
Controlling effect of vector and scalar crossed double-Ma breathers in a partially nonlocal nonlinear medium with a linear potential	80
Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques	80
Nondegenerate solitons of 2-coupled mixed derivative nonlinear Schrödinger equations	78
An improved dynamic model of spur gear transmission considering coupling effect between gear neighboring teeth	77
Analysis and design of a novel and compact X-structured vibration isolation mount (X-Mount) with wider quasi-zero-stiffness range	76
The variable separation solution, fractal and chaos in an extended coupled (2+1)-dimensional Burgers system	75
Hyperchaotic memristive ring neural network and application in medical image encryption	75
Studies on certain bilinear form, N-soliton, higher-order breather, periodic-wave and hybrid solutions to a (3+1)-dimensional shallow water wave equation with time-dependent coefficients	74
Wronskian, Gramian, Pfaffian and periodic-wave solutions for a (3+1)-dimensional generalized nonlinear evolution equation arising in the shallow water waves	74
A robust image encryption scheme using chaotic tent map and cellular automata	73
Image encryption algorithm with circle index table scrambling and partition diffusion	73
Color image encryption based on cross 2D hyperchaotic map using combined cycle shift scrambling and selecting diffusion	72
Human mobility and COVID-19 initial dynamics	71
Soliton and breather molecules in few-cycle-pulse optical model	71
Nonlinear control of logic structure of all-optical logic devices using soliton interactions	69
Painlevé integrability and lump solutions for two extended (3 + 1)- and (2 + 1)-dimensional Kadomtsev–Petviashvili equations	69
Comprehensive theoretical and experimental investigation of the rotational impact energy harvester with the centrifugal softening effect	69
A fractional-order multistable locally active memristor and its chaotic system with transient transition, state jump	69
A tristable locally active memristor and its application in Hopfield neural network	68
Interaction dynamics of hybrid solitons and breathers for extended generalization of Vakhnenko equation	67
Periodic soliton interactions for higher-order nonlinear Schrödinger equation in optical fibers	67
A locally active discrete memristor model and its application in a hyperchaotic map	66
A feasible neuron for estimating the magnetic field effect	65
New $$(3+1)$$-dimensional Painlevé integrable fifth-order equation with third-order temporal dispersion	65
Lump, soliton, and interaction solutions to a generalized two-mode higher-order nonlinear evolution equation in plasma physics	64
The interference wave and the bright and dark soliton for two integro-differential equation by using BNNM	63
A new (3 + 1)-dimensional Schrödinger equation: derivation, soliton solutions and conservation laws	63
Generation and transformation of dark solitons, anti-dark solitons and dark double-hump solitons	61
The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension	61
A review of the mechanical inerter: historical context, physical realisations and nonlinear applications	61
A second-order stochastic resonance method enhanced by fractional-order derivative for mechanical fault detection	61
Vibration control combining nonlinear isolation and nonlinear absorption	60
Dynamics and control of COVID-19 pandemic with nonlinear incidence rates	60
Memristive electromagnetic induction effects on Hopfield neural network	60
N-order rogue waves and their novel colliding dynamics for a transient stimulated Raman scattering system arising from nonlinear optics	58

Nonlinear targeted energy transfer: state of the art and new perspectives	58
Design of pseudo-random number generator from turbulence padded chaotic map	58
Forecast analysis of the epidemics trend of COVID-19 in the USA by a generalized fractional-order SEIR model	57
Dynamic event-based reliable dissipative asynchronous control for stochastic Markov jump systems with general conditional probabilities	57
Nonlinear phenomena of contact in multibody systems dynamics: a review	57
COVID-19 pandemic in India: a mathematical model study	56
An improved quasi-zero stiffness isolator with two pairs of oblique springs to increase isolation frequency band	55
Bistable attachments for wideband nonlinear vibration attenuation in a metamaterial beam	55
Nonlinear model predictive control with logic constraints for COVID-19 management	54
N-fold Darboux transformation and solitonic interactions for the Kraenkel–Manna–Merle system in a saturated ferromagnetic material	54
Quantum logistic image encryption algorithm based on SHA-3 and RSA	54
Biophysical mechanism of signal encoding in an auditory neuron	54
Synchronization and chimeras in a network of photosensitive FitzHugh–Nagumo neurons	54
Multiple rogue wave, breather wave and interaction solutions of a generalized (3 + 1)-dimensional variable-coefficient nonlinear wave equation	53
Accurate modeling and analysis of a typical nonlinear vibration isolator with quasi-zero stiffness	52
Epidemic model of COVID-19 outbreak by inducing behavioural response in population	52
Bidirectional solitons and interaction solutions for a new integrable fifth-order nonlinear equation with temporal and spatial dispersion	52
High-order sliding mode observer-based trajectory tracking control for a quadrotor UAV with uncertain dynamics	51
Dynamics of optical solitons and nonautonomous complex wave solutions to the nonlinear Schrodinger equation with variable coefficients	51
Trends, directions for further research, and some open problems of fractional calculus	51
Dynamics of the double-beam piezo–magneto–elastic nonlinear wind energy harvester exhibiting galloping-based vibration	51
A health performance evaluation method of multirotors under wind turbulence	50
Nonlinear waves behaviors for a coupled generalized nonlinear Schrödinger–Boussinesq system in a homogeneous magnetized plasma	50
Effective amplification of optical solitons in high power transmission systems	50
Lax pair, Darboux transformation, breathers and rogue waves of an $$\pmb {N}$$-coupled nonautonomous nonlinear Schrödinger system for an optical fiber or a plasma	50
Sliding mode control for nonlinear stochastic systems with Markovian jumping parameters and mode-dependent time-varying delays	50
M-lump, high-order breather solutions and interaction dynamics of a generalized $$(2 + 1)$$-dimensional nonlinear wave equation	50
Fixed-time SOSM controller design with output constraint	49
Nondegenerate soliton dynamics of nonlocal nonlinear Schrödinger equation	49
Clarify the physical process for fractional dynamical systems	49
Mathematical model of COVID-19 with comorbidity and controlling using non-pharmaceutical interventions and vaccination	49
Nonlinear dynamic response of sandwich plates with functionally graded auxetic 3D lattice core	48
How to wake up the electric synapse coupling between neurons?	48
Reproduce the biophysical function of chemical synapse by using a memristive synapse	48
A S-type bistable locally active memristor model and its analog implementation in an oscillator circuit	48
A novel perturbation method to reduce the dynamical degradation of digital chaotic maps	48
Abundant vector soliton prediction and model parameter discovery of the coupled mixed derivative nonlinear Schrödinger equation	48
Kadomtsev–Petviashvili hierarchy: two integrable equations with time-dependent coefficients	48
Effects of dispersion terms on optical soliton propagation in a lossy fiber system	48
How to compute invariant manifolds and their reduced dynamics in high-dimensional finite element models	47
Adaptive attack-resilient control for Markov jump system with additive attacks	47
Dark wave, rogue wave and perturbation solutions of Ivancevic option pricing model	47
Vector soliton pairs for a coupled nonautonomous NLS model with partially nonlocal coupled nonlinearities under the external potentials	47
Solving localized wave solutions of the derivative nonlinear Schrödinger equation using an improved PINN method	47
Fixed-time disturbance observer-based robust fault-tolerant tracking control for uncertain quadrotor UAV subject to input delay	46
Adaptive model-free synchronization of different fractional-order neural networks with an application in cryptography	46
Parameter identification for discrete memristive chaotic map using adaptive differential evolution algorithm	46
Rare and extreme events: the case of COVID-19 pandemic	46
Adaptive robust decoupling control of multi-arm space robots using time-delay estimation technique	46
The integrable Boussinesq equation and it’s breather, lump and soliton solutions	45
Chebyshev spectral methods for multi-order fractional neutral pantograph equations	45
Analysis of lumps, single-stripe, breather-wave, and two-wave solutions to the generalized perturbed-KdV equation by means of Hirota’s bilinear method	45
Nonlinear dynamic analysis of an epidemiological model for COVID-19 including public behavior and government action	45
Isolation performance of a quasi-zero stiffness isolator in vibration isolation of a multi-span continuous beam bridge under pier base vibrating excitation	45
Data-driven-based event-triggered optimal control of unknown nonlinear systems with input constraints	44
A ship motion forecasting approach based on empirical mode decomposition method hybrid deep learning network and quantum butterfly optimization algorithm	44
Optimal model-free backstepping control for a quadrotor helicopter	44
Adaptive neural network consensus tracking control for uncertain multi-agent systems with predefined accuracy	44
Regulating memristive neuronal dynamical properties via excitatory or inhibitory magnetic field coupling	44
Use of generalized refined composite multiscale fractional dispersion entropy to diagnose the faults of rolling bearing	44
A nonlinear dynamic vibration model of cylindrical roller bearing considering skidding	43
Ultra-low frequency energy harvesting using bi-stability and rotary-translational motion in a magnet-tethered oscillator	43
A sliding mode observer for robust fault reconstruction in a class of nonlinear non-infinitely observable descriptor systems	43
Co-evolution spreading of multiple information and epidemics on two-layered networks under the influence of mass media	43
Nonlinear dynamics of acoustic bubbles excited by their pressure-dependent subharmonic resonance frequency: influence of the pressure amplitude, frequency, encapsulation and multiple bubble interactio	43
Mathematical modeling and optimal intervention strategies of the COVID-19 outbreak	43
Stabilization of the passive walking dynamics of the compass-gait biped robot by developing the analytical expression of the controlled Poincaré map	42
Stable transmission characteristics of double-hump solitons for the coupled Manakov equations in fiber lasers	42
Dynamics of diverse data-driven solitons for the three-component coupled nonlinear Schrödinger model by the MPS-PINN method	42
A new SAIR model on complex networks for analysing the 2019 novel coronavirus (COVID-19)	42
Numerical simulation and stability analysis of a novel reaction–diffusion COVID-19 model	42
Nonlinear vibration effects on the fatigue life of fluid-conveying pipes composed of axially functionally graded materials	42
The numerical modeling of rotor–stator rubbing in rotating machinery: a comprehensive review	41
Remote sensing image compression and encryption based on block compressive sensing and 2D-LCCCM	41
Continuous adaptive integral-type sliding mode control based on disturbance observer for PMSM drives	41
Integrable (3+1)-dimensional Ito equation: variety of lump solutions and multiple-soliton solutions	41
An efficient dual-layer cross-coupled chaotic map security-based multi-image encryption system	41
Design of a metastructure for vibration isolation with quasi-zero-stiffness characteristics using bistable curved beam	41
Experimental and numerical studies of intestinal frictions for propulsive force optimisation of a vibro-impact capsule system	40
Cryptanalysis and enhancement of an image encryption scheme based on a 1-D coupled Sine map	40

A fractional-order SEIHDR model for COVID-19 with inter-city networked coupling effects	39
A nonlinear vibration isolator with quasi-zero-stiffness inspired by Miura-origami tube	39
Nonlinear forced vibrations of rotating cylindrical shells under multi-harmonic excitations in thermal environment	39
Design criteria of bistable nonlinear energy sink in steady-state dynamics of beams and plates	39
Collision dynamics of three-solitons in an optical communication system with third-order dispersion and nonlinearity	38
Epidemic dynamics of influenza-like diseases spreading in complex networks	38
Observer-based adaptive fuzzy finite-time prescribed performance tracking control for strict-feedback systems with input dead-zone and saturation	38
Dynamic modeling and trajectory tracking control method of segmented linkage cable-driven hyper-redundant robot	38
Impact of information diffusion on epidemic spreading in partially mapping two-layered time-varying networks	37
Assessing the effect of containment measures on the spatio-temporal dynamic of COVID-19 in Italy	37
Bispectral mode decomposition of nonlinear flows	37
2D mixed pseudo-random coupling PS map lattice and its application in S-box generation	36
Distributed adaptive neural network consensus for a class of uncertain nonaffine nonlinear multi-agent systems	36
Bilinear form, soliton, breather, hybrid and periodic-wave solutions for a (3+1)-dimensional Korteweg–de Vries equation in a fluid	36
An improved quasi-zero stiffness vibration isolation system utilizing dry friction damping	36
Review and new theoretical perspectives on active disturbance rejection control for uncertain finite-dimensional and infinite-dimensional systems	36
Nonlinear vibrations and damping of fractional viscoelastic rectangular plates	36
Consensus of nonlinear multiagent systems with intermittent dynamic event-triggered protocols	36
Bilinear Bäcklund transformation, Lax pair and interactions of nonlinear waves for a generalized (2 + 1)-dimensional nonlinear wave equation in nonlinear optics/fluid mechanics/plasma physics	36
Model order reduction based on direct normal form: application to large finite element MEMS structures featuring internal resonance	35
Bilinear form, solitons, breathers, lumps and hybrid solutions for a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation	35
An exploration of fractal-based prognostic model and comparative analysis for second wave of COVID-19 diffusion	35
An adjustable visual image cryptosystem based on 6D hyperchaotic system and compressive sensing	35
Nonlinear thermal behaviors of the inter-shaft bearing in a dual-rotor system subjected to the dynamic load	35
Nonlinear vibrations of rotating pretwisted composite blade reinforced by functionally graded graphene platelets under combined aerodynamic load and airflow in tip clearance	35
Spread mechanism and control strategy of social network rumors under the influence of COVID-19	34
Soliton solutions of the nonlinear sine-Gordon model with Neumann boundary conditions arising in crystal dislocation theory	34
A novel long short-term memory neural-network-based self-excited force model of limit cycle oscillations of nonlinear flutter for various aerodynamic configurations	34
Interpreting, analysing and modelling COVID-19 mortality data	34
Gradient-optimized physics-informed neural networks (GOPINNs): a deep learning method for solving the complex modified KdV equation	34
Delay-induced chaos and its possible control in a seasonally forced eco-epidemiological model with fear effect and predator switching	34
Localized waves and mixed interaction solutions with dynamical analysis to the Gross–Pitaevskii equation in the Bose–Einstein condensate	34
COVID-19: data-driven dynamics, statistical and distributed delay models, and observations	34
The role of punishment in the spatial public goods game	34
Chaotic resonance in Izhikevich neural network motifs under electromagnetic induction	33
Nonlinear oscillations of electrically driven aniso-visco-hyperelastic dielectric elastomer minimum energy structures	33
Geometrical patterns of time variable Kadomtsev–Petviashvili (I) equation that models dynamics of waves in thin films with high surface tension	33
Nonlinear vibration and dynamic stability analysis of an axially moving beam with a nonlinear energy sink	33
Permutation entropy-based 2D feature extraction for bearing fault diagnosis	33
Vector breathers, rogue and breather-rogue waves for a coupled mixed derivative nonlinear Schrödinger system in an optical fiber	33
Nonlinear energy-based control of soft continuum pneumatic manipulators	32
Global multistability and analog circuit implementation of an adapting synapse-based neuron model	32
Robust trajectory tracking control of marine surface vessels with uncertain disturbances and input saturations	32
A new locally active memristive synapse-coupled neuron model	32
Distributed fixed-time optimization for multi-agent systems over a directed network	32
Pseudo-random number generator based on a generalized conservative Sprott-A system	32
A new type-3 fuzzy predictive controller for MEMS gyroscopes	32
Dark and bright soliton solutions and computational modeling of nonlinear regularized long wave model	32
Extended state observer-based adaptive prescribed performance control for a class of nonlinear systems with full-state constraints and uncertainties	32
Comparison of nonlinear mappings for reduced-order modelling of vibrating structures: normal form theory and quadratic manifold method with modal derivatives	32
Fixed-time adaptive event-triggered tracking control of uncertain nonlinear systems	32
Simplified coded dispersion entropy: a nonlinear metric for signal analysis	32
Effects of control measures on the dynamics of COVID-19 and double-peak behavior in Spain	32
Self-delayed feedback car-following control with the velocity uncertainty of preceding vehicles on gradient roads	32
Soliton, breather and rogue wave solutions of the coupled Gerdjikov–Ivanov equation via Darboux transformation	31
Resonant multiple wave, periodic wave and interaction solutions of the new extended (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation	31
Spatiotemporal dynamics induced by nonlocal competition in a diffusive predator-prey system with habitat complexity	31
Multistable dynamics in a Hopfield neural network under electromagnetic radiation and dual bias currents	31
Mathematical modeling and mechanisms of pattern formation in ecological systems: a review	31
Light-powered self-excited motion of a liquid crystal elastomer rotator	31
Adaptive fuzzy finite-time control of stochastic nonlinear systems with actuator faults	31
Integrability, multi-solitons, breathers, lumps and wave interactions for generalized extended Kadomtsev–Petviashvili equation	31
Multilayer neural networks-based control of underwater vehicles with uncertain dynamics and disturbances	30
Vaccination control of an epidemic model with time delay and its application to COVID-19	30
Theoretical and experimental study of an enhanced nonlinear energy sink	30
Dynamical analysis of an improved FitzHugh-Nagumo neuron model with multiplier-free implementation	30
Firing mechanism based on single memristive neuron and double memristive coupled neurons	30
Hierarchical diversity entropy for the early fault diagnosis of rolling bearing	30
A review on nonlinear energy sinks: designs, analysis and applications of impact and rotary types	30
Smooth nonlinear fitting scheme for analog multiplierless implementation of Hindmarsh–Rose neuron model	30
Modeling tangential friction based on contact pressure distribution for predicting dynamic responses of bolted joint structures	30
Non-singular multi-complexiton wave to a generalized KdV equation	30
Bursting vibration-based energy harvesting	30
ANS-net: anti-noise Siamese network for bearing fault diagnosis with a few data	30
Sliding mode control for uncertain active vehicle suspension systems: an event-triggered $$\varvec{\mathcal {H}}_{\infty }$$ control scheme	30
Finite-time adaptive neural resilient DSC for fractional-order nonlinear large-scale systems against sensor-actuator faults	30
Ultra-broadband piezoelectric energy harvesting via bistable multi-hardening and multi-softening	30
Steady-state response of a viscoelastic beam with asymmetric elastic supports coupled to a lever-type nonlinear energy sink	30
Study on dynamical behavior of multiple lump solutions and interaction between solitons and lump wave	30
Robust control of reaction wheel bicycle robot via adaptive integral terminal sliding mode	29
Social dynamics and Parrondo’s paradox: a narrative review	29
Fixed-time integral sliding mode control of a high-order nonlinear system	29
Dynamic analysis of 1-dof and 2-dof nonlinear energy sink with geometrically nonlinear damping and combined stiffness	29
Image encryption algorithm with matrix semi-tensor product	29
Wave propagation in a network of extended Morris–Lecar neurons with electromagnetic induction and its local kinetics	29
A memristive system and its applications in red–blue 3D glasses and image encryption algorithm with DNA variation	29
Magneto-electro-elastic modelling and nonlinear vibration analysis of bi-directional functionally graded beams	29
Breathers and rogue waves on the double-periodic background for the reverse-space-time derivative nonlinear Schrödinger equation	29
Exact solutions with elastic interactions for the (2 $$+$$ 1)-dimensional extended Kadomtsev–Petviashvili equation	29
Mittag–Leffler stability of nabla discrete fractional-order dynamic systems	29
A novel sliding surface design for predefined-time stabilization of Euler–Lagrange systems	29
Optical solitons and bifurcation analysis in fiber Bragg gratings with Lie symmetry and Kudryashov’s approach	29
Bursting oscillations with delayed C-bifurcations in a modified Chua’s circuit	28
Memristive hyperchaos secure communication based on sliding mode control	28
Bifurcation analysis, chaotic behaviors, sensitivity analysis, and soliton solutions of a generalized Schrödinger equation	28