Chaos, Solitons & Fractals

2002 - 2025

Current editor(s): Stefano Boccaletti and Stelios Bekiros

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2024, volume 189, articles P2

Wavefunction engineering using Mandelbrot, multicorn, and Koch's snowflake fractal quantum rings to control the persistent current

Davood Haji Taghi Tehrani, M. Solaimani and M.R. Fathollahi

True random number generator using stochastic noise signal of memristor with variation tolerance

Dayeon Yu, Suhyeon Ahn, Sangwook Youn, Jinwoo Park and Hyungjin Kim

Generalized fined-grained multiscale information entropy with multi-feature extraction and its application in phase space reconstruction

Yupeng Shen, Yaan Li, Weijia Li and Quanmao Yao

Auto-resonance process under the interaction of solitons with external force and dissipation

Marcelo V. Flamarion and Efim Pelinovsky

Analysis of a stochastic SEIS epidemic model motivated by Black–Karasinski process: Probability density function

Baoquan Zhou and Ningzhong Shi

Analytical properties and related inequalities derived from multiplicative Hadamard k-fractional integrals

Ziyi Zhou and Tingsong Du

Determination of a time dependent source in semilinear pseudoparabolic equations with Caputo fractional derivative

Kh. Khompysh

Nonlinear sensitivity and optimization of heat transfer and drag in power law fluid flow over a permeable wedge with variable magnetic field and thermal radiation effects

Wajiha Waheed, Abuzar Ghaffari, Irfan Mustafa and Rab Nawaz

The impact of social noise on the majority rule model across various network topologies

Roni Muslim, Didi Ahmad Mulya, Zulkaida Akbar and Rinto Anugraha Nqz

Analysis of an opinion dynamics model coupled with an external environmental dynamics

Anthony Couthures, Vineeth Satheeskumar Varma, Samson Lasaulce and Irinel - Constantin Morărescu

Deep sparse autoencoders-based community detection and resilience analysis of interdependent infrastructure networks

Shuliang Wang, Jin Wang, Shengyang Luan and Bo Song

Fast and slow dynamical behaviors of delayed-coupled thermosensitive neurons under electromagnetic induction

Yansu Ji and Xiaochen Mao

A novel fractional-order grey Euler prediction model and its application in short-term traffic flow

Yuxin Song, Huiming Duan and Yunlong Cheng

A novel neural networks with memristor coupled memcapacitor-synapse neuron

Fan Shi, Yinghong Cao, Santo Banerjee, Adil M. Ahmad and Jun Mou

Analytical approximation of dynamic responses of random parameter nonlinear systems based on stochastic perturbation-Galerkin method

Bin Huang, Cihang Ma, Yejun Li, Zhifeng Wu and Heng Zhang

Resonant responses and double-parameter multi-pulse chaotic dynamics of FG-GP reinforced rotating pre-twisted composite laminated blade under combined transverse aerodynamic force and parametric excitations

Y.Z. Lian, W. Zhang and Y.F. Zhang

Stability analysis of an axially moving viscoelastic beam under transverse magnetic fields and thermal loads

Sihan Wu, Xudong Gu, Bingxin Zhao and Zichen Deng

Unraveling dengue dynamics with data calibration from Palu and Jakarta: Optimizing active surveillance and fogging interventions

Dipo Aldila, Joseph Páez Chávez, Chidozie W. Chukwu, Athaya Yumna Fathiyah, Juni Wijayanti Puspita, Kartika A. Dimar Setio, Ahmad Fuady and Putri Zahra Kamalia

Impact of directionality on the emergence of Turing patterns on m-directed higher-order structures

Marie Dorchain, Wilfried Segnou, Riccardo Muolo and Timoteo Carletti

New disordered phases of the (s,1/2)-mixed spin Ising model for arbitrary spin s

Hasan Akın

Propagation dynamics of the second-order chirped circular Pearcey Gaussian vortex beam in the fractional nonlinear Schrödinger equation

Shangling He, Xi Peng, Yingji He, Chun Shan and Dongmei Deng

Transition from circular to spiral waves and from Mexican hat to upside-down Mexican hat-solutions: The cases of local and nonlocal λ−ω reaction-diffusion-convection fractal systems with variable coefficients

Rami Ahmad El-Nabulsi

Numerical approach and physical description for a two-capacitive neuron and its adaptive network dynamics

Yixuan Chen, Qun Guo, Xiaofeng Zhang and Chunni Wang

Jointed pendulums driven by a neural circuit, electromechanical arm model approach

Yitong Guo, Chunni Wang and Jun Ma

Boundary disturbance rejection for Caputo-Hadamard fractional heat equations via ADRC approach

Rui-Yang Cai and Hua-Cheng Zhou

Activation energy and non-Darcy effects on magnetized Jeffery-Hamel (JH) flow in convergent/divergent channels

Subhan Ullah, Amir Ali, Ikram Ullah, Mohammad Mahtab Alam and Zareen A. Khan

2024, volume 189, articles P1

Chaotic dynamics and synchronization under tripartite couplings: Analyses and experiments using single-transistor oscillators as metaphors of neural dynamics

Ludovico Minati, Laura Sparacino, Luca Faes, Hiroyuki Ito, Chunbiao Li, Pedro A. Valdes-Sosa, Mattia Frasca and Stefano Boccaletti

Disordered FPUT-α Hamiltonian Lattices: Recurrence breakdown and chaotic behavior

Zulkarnain,, H. Susanto and C.G. Antonopoulos

A secondary optimization strategy in stochastic resonance modelling for the detection of unknown bearing faults

Mengdi Li, Jinfeng Huang, Peiming Shi, Feibin Zhang, Fengshou Gu and Fulei Chu

Stability and bipartite synchronization of fractional-order coupled reaction–diffusion neural networks under unbalanced graph

Rixu Hao, Yongqing Yang, Fengyi Liu and Boling Zhou

Single direction, grid and spatial multi-scroll attractors in Hopfield neural network with the variable number memristive self-connected synapses

Qiuzhen Wan, Qiao Yang, Tieqiao Liu, Chaoyue Chen and Kun Shen

A new two-parameter controllable multi-scroll 4D Hamiltonian conservative hyperchaotic system with improved nested COS-PWL function

Tingkai Zhao, Xu Sun, Zhenyi Fan and Baoxiang Du

Multiple-image encryption algorithm based on a new composite chaotic system and 3D coordinate matrix

Qisu Gao and Xiaoqiang Zhang

Application of the matrix element method: A mode-matching approach for wave-bearing cavities in complex media

Hazrat Bilal and Muhammad Afzal

Transition and coexistence of Turing pattern, Turing-like pattern and spiral waves in a discrete-time predator–prey model

Huimin Zhang, Jian Gao, Changgui Gu, Chuansheng Shen and Huijie Yang

Integrating Virtual and Physical Interactions through higher-order networks to control epidemics

Santiago Lamata-Otín, Adriana Reyna-Lara and Jesús Gómez-Gardeñes

Three limit cycles in the Kim–Forger model of the mammalian circadian clock

Xin Pei, Jiang-Hong Hu, Mingtao Li, Yuchen Ding, Juping Zhang and Yongxin Zhang

Fractal dimensions of discrete Moran sets

Yiqi Yao, Caimin Du and Lifeng Xi

Probing Topological Superconductivity of oxide nanojunctions using fractional Shapiro steps

Claudio Guarcello, Alfonso Maiellaro, Jacopo Settino, Irene Gaiardoni, Mattia Trama, Francesco Romeo and Roberta Citro

Adaptive dynamic event-triggered asymptotic control for uncertain nonlinear systems

Yongchao Liu and Ning Zhao

Driving a Josephson Traveling Wave Parametric Amplifier into chaos: Effects of a non-sinusoidal current–phase relation

Claudio Guarcello, Carlo Barone, Giovanni Carapella, Veronica Granata, Giovanni Filatrella, Andrea Giachero and Sergio Pagano

Analysis of nonlinear complex heat transfer MHD flow of Jeffrey nanofluid over an exponentially stretching sheet via three phase artificial intelligence and Machine Learning techniques

Ahmad Zeeshan, Nouman Khalid, Rahmat Ellahi, M.I. Khan and Sultan Z. Alamri

Simultaneous identification of the unknown source term and initial value for the time fractional diffusion equation with local and nonlocal operators

Li Qiao, Fan Yang and Xiaoxiao Li

Dynamical analysis of the Rulkov model with quasiperiodic forcing

Gaolei Li, Jicheng Duan, Zhixuan Yue, Zhe Li and Denghui Li

Jams and phase transitions in heterogeneous lattice model integrating the continuous delayed feedback control to boycott cyber-attacks under connected autonomous and human driven vehicles environment

Guanghan Peng, Meilan Zhu and Huili Tan

Memory of fracture in information geometry

Mitsuhiro Hirano and Hiroyuki Nagahama

Design and analysis of a novel differential chaos shift keying system with joint three-dimensional index modulation

Lifang He, Xinyu Xiong and Yongqi Guo

A novel adaptive predefined-time sliding mode control scheme for synchronizing fractional order chaotic systems

Yunkang Sun, Yuquan Chen, Bing Wang and Cheng Ma

Nonlinear dynamics and sliding mode control for global fixed-time synchronization of a novel 2 × 2 memristor-based cellular neural network

Yuman Zhang and Yuxia Li

Elite women's soccer match demand can be described using complexity-based analyses and multifractals

Nicolas Babault, Gaelyann Rodot, Carole Cometti and Denis César Leite Vieira

Spatiotemporal patterns in a 2D lattice of Hindmarsh–Rose neurons induced by high-amplitude pulses

J.S. Ram, S.S. Muni and I.A. Shepelev

Ratchet current and scaling properties in a nontwist mapping

Matheus Rolim Sales, Daniel Borin, Leonardo Costa de Souza, José Danilo Szezech , Ricardo Luiz Viana, Iberê Luiz Caldas and Edson Denis Leonel

Subcombination internal resonance of the additive type in the response dynamics of micromachined resonators crossing the impacting threshold

Laura Ruzziconi, Nizar Jaber, Amal Z. Hajjaj and Mohammad I. Younis

An improved lattice Boltzmann model for variable-order time-fractional generalized Navier-Stokes equations with applications to permeability prediction

Junjie Ren, Hao Lei and Jie Song

Pseudo-phase difference guides additional connection between oscillators for synchrony

Daekyung Lee, Jong-Min Park and Heetae Kim

Stocking of herbivorous fish to mitigate algal bloom in water bodies: A modeling approach

Jyoti Maurya, Santo Banerjee and A.K. Misra

Lower bounds of decay rates for the MHD micropolar equations

Felipe W. Cruz and Lorena B.S. Freitas

Nonlinear chaotic Lorenz-Lü-Chen fractional order dynamics: A novel machine learning expedition with deep autoregressive exogenous neural networks

Shahzaib Ahmed Hassan, Muhammad Junaid Ali Asif Raja, Chuan-Yu Chang, Chi-Min Shu, Muhammad Shoaib, Adiqa Kausar Kiani and Muhammad Asif Zahoor Raja

Collective motion with the self-propelled directional reversals effect

Changyun Wang, C.R. Li, W. Guo and L.C. Du

The warning effect of persistent defection strategy promotes cooperation in spatial prisoner’s dilemma game

Yan Bi, Qingyi Hao and Wenjun Wu

Two-component model of a microtubule in a semi-discrete approximation

Slobodan Zdravković, Aleksandr N. Bugay, Slobodan Zeković, Dragana Ranković and Jovana Petrović

Dynamics analysis of time-delayed nonlinear system with asymmetric stiffness

Xinliang Liu, Shaoke Wan, Bin Fang and Xiaohu Li

Parameter estimation in the stochastic SIR model via scaled geometric Brownian motion

J.A. Sánchez-Monroy, Javier Riascos-Ochoa and Abel Bustos

Exploring the interplay of biodiversity and mutation in cyclic competition systems

Junhyeok Choi, Junpyo Park and Bongsoo Jang

Excitation and manipulation of super cavity solitons in multi-stable passive Kerr resonators

Pengxiang Wang, Jianxing Pan, Tianye Huang, Shengbo Xu, Ran Xia, Julien Fatome, Bertrand Kibler, Carlos Mas-Arabi and Gang Xu

Entanglement between indirectly coupled modes in a coupled opto-magnomechanical system

Xi-Yao Ma, Hong-Jie Du, Guo-Zhu Song and Jin-Liang Guo

Community detection in directed networks based on network embeddings

Guihai Yu, Yang Jiao, Matthias Dehmer and Frank Emmert-Streib

Stability of nonlinear delayed impulsive control systems via step-function method

Yinuo Wang, Chuandong Li, Hongjuan Wu and Hao Deng

Novel Tabu learning neuron model with variable activation gradient and its application to secure healthcare

Donghua Jiang, Zeric Tabekoueng Njitacke, Guoqiang Long, Jan Awrejcewicz, Mingwen Zheng and Lei Cai

Parameters estimation and uncertainty assessment in the transmission dynamics of rabies in humans and dogs

Mfano Charles, Sayoki G. Mfinanga, G.A. Lyakurwa, Delfim F.M. Torres and Verdiana G. Masanja

Diffusion-driven instabilities in a tri-trophic food web model: From Turing to non-Turing patterns and waves

Bhaskar Chakraborty, Sounov Marick and Nandadulal Bairagi

Modulating propagation of Parkinsonian beta oscillations with transcranial direct current stimulation: A computational study

Xiaomin Wang, Ying Yu and Qingyun Wang

Design of chaotic Young's double slit experiment optimization heuristics for identification of nonlinear muscle model with key term separation

Khizer Mehmood, Zeshan Aslam Khan, Naveed Ishtiaq Chaudhary, Khalid Mehmood Cheema, Bazla Siddiqui and Muhammad Asif Zahoor Raja

Dynamical sensitivity of a three-layer microsystem under the influence of the Casimir force in a ferrofluid

M. Mirzaei, A.A. Masoudi, F. Tajik and G. Palasantzas

A novel image encryption algorithm with anti-tampering attack capability

Chengye Zou, Yubao Shang, Yongwei Yang, Changjun Zhou and Yunong Liu

Dynamical effects of low-frequency and high-frequency current stimuli in a memristive Morris–Lecar neuron model

Quan Xu, Kai Wang, Chengtao Feng, Weiwei Fan and Ning Wang

Improving resilience of cyber physical power networks against Time Synchronization Attacks (TSAs) using deep learning and spline interpolation with real-time validation

Soma Bhattacharya, Ebha Koley and Subhojit Ghosh

Optimal resilient tracking control of switched systems under denial-of-service attacks

Chen Chen and Lijie Wang

Self-triggered consensus resilient control for multi-agent systems against sensor deception attacks based on a single parameter learning method

Junwen Xiao and Yongchao Liu

Chaos and regularities in cavity assisted two-channel nonlinear coupler

Firoz Chogle, Seba Sara Varghese, Abdel-Baset M.A. Ibrahim, Awadhesh Prasad and Hichem Eleuch

Shock waves and adiabatic trapping in relativistic quantum degenerate plasmas: Exploring periodic, quasiperiodic and chaotic behavior

Zeeshan Iqbal, H.A. Shah, M.N.S. Qureshi and Eihab M. Abdel-Rahman

A reinforced reservoir computer aided by an external asymmetric dual-path-filtering cavity laser

Deyu Cai, Penghua Mu, Yu Huang, Pei Zhou and Nianqiang Li

Chaotic self-oscillation of liquid crystal elastomer double-line pendulum under a linear temperature field

Xin Sun, Dali Ge, Kai Li and Peibao Xu

New aspects of black box conditional gradient: Variance reduction and one point feedback

Andrey Veprikov, Alexander Bogdanov, Vladislav Minashkin and Aleksandr Beznosikov

Generating digital chaotic systems of the simplest structure via a strongly connected graph inverse approach

Qianxue Wang, Dongsheng Kuang and Simin Yu

Nonlinear harmonic resonant behaviors and bifurcation in a Two Degree-of-Freedom Duffing oscillator coupled system of Tension Leg Platform type Floating Offshore Wind Turbine

Ouming Su, Yan Li, Guoyan Li, Yiwen Cui, Haoran Li, Bin Wang, Hang Meng, Yaolong Li and Jinfeng Liang

Chaotic semigroups for a higher order partial differential equation in Herzog-type space of analytic functions

A. Taqbibt, M. Chaib, M. Elomari and S. Melliani

Symmetry group based domain decomposition to enhance physics-informed neural networks for solving partial differential equations

Ye Liu, Jie-Ying Li, Li-Sheng Zhang, Lei-Lei Guo and Zhi-Yong Zhang

Strange attractors, nonlinear dynamics and abundant novel soliton solutions of the Akbota equation in Heisenberg ferromagnets

Mohammad Alqudah, Maalee AlMheidat, M.M. Alqarni, Emad E. Mahmoud and Shabir Ahmad

A fast matrix autoregression algorithm based on Tucker decomposition for online prediction of nonlinear real-time taxi-hailing demand without pre-training

Zhihao Xu, Zhiqiang Lv, Benjia Chu and Jianbo Li

A network method to analyze compound extreme events: Risk enhancement relationship and trigger causal relationship in high voice traffic and high data throughput events

Li-Na Wang, Hao-Ran Liu, Yu-Wen Huang, Chen-Rui Zang and Jun Wang

Application of hybrid strategies of complex network attack and defense games

Zhe Li, Jin Liu, Jiaqi Ren, Yibo Dong and Weili Li

Hybrid control design for nonlinear chaotic semi-Markov jump systems via fault alarm approach

R. Sakthivel, R. Abinandhitha, T. Satheesh and O.M. Kwon

Data driven cost-sensitive boosted tree for interpretable banking systemic risk prediction

Meng Xia, Zhijie Wang and Wanan Liu

Particle swarm optimization with historical return decay enhances cooperation in public goods games with investment risks

Hongwei Kang, Xin Li, Yong Shen, Xingping Sun and Qingyi Chen

Impulsive quasi-containment control in stochastic heterogeneous multiplex networks

Xin Jin, Zhengxin Wang and Xiaojie Chen

Dynamic characteristics and conversion process of solitons in a Mamyshev oscillator

Yuhe Dong, Xingliang Li, Mengmeng Han, Shumin Zhang and Chaoran Wang

Study on a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation in nonlinear physics: Multiple soliton solutions, lump solutions, and breather wave solutions

Abdul-Majid Wazwaz

Synthesis of a hybrid control algorithm for chaotifying mechanical systems

Swapnil Mahadev Dhobale and Shyamal Chatterjee

A non-singleton type-3 neuro-fuzzy fixed-time synchronizing method

Hamid Taghavifar, Ardashir Mohammadzadeh and Chunwei Zhang

Azimuthally dependent spontaneous emission from a coherently microwave-field driven four-level atom-light coupling scheme

Muqaddar Abbas, Seyyed Hossein Asadpour, Rahmatullah,, Feiran Wang, Hamid R. Hamedi and Pei Zhang

Complex dynamics in tick-borne disease transmission: A Filippov-type control strategy model with multiple time delays

Ning Yu and Xue Zhang

Percolation behavior of partially interdependent networks with capacity and loads

Mengjiao Chen, Niu Wang, Daijun Wei and Changcheng Xiang

Identifying influential nodes in social networks via improved Laplacian centrality

Xiaoyu Zhu and Rongxia Hao

Evolution of strategies in evolution games on small-world networks and applications

Chengyan Liu, Wangyong Lv, Xinzexu Cheng, Yihao Wen and Xiaofeng Yang

Adaptive practical prescribed-time control for uncertain nonlinear systems with time-varying parameters

Tianping Zhang and Wei Zhang

Effects of correlated noise on the excitation of robust breathers in an ac-driven, lossy sine–Gordon system

Giovanni Di Fresco, Duilio De Santis, Claudio Guarcello, Bernardo Spagnolo, Angelo Carollo and Davide Valenti

Prescribed-time multi-coalition Nash equilibrium seeking by event-triggered communication

Mengwei Sun, Lu Ren, Jian Liu and Changyin Sun

Eco-evolutionary feedbacks promotes species coexistence in the fig-wasp mutualism with Allee effect

Lin Wang, Yin-Ling Liu, Xiao-Fen Lin and Rui-Wu Wang

Spiral wave chimeras in nonlocally coupled excitable FitzHugh–Nagumo neurons

Yang Li, Haihong Li, Shun Gao, Yirui Chen, Qionglin Dai and Junzhong Yang

A neural diffusion model for identifying influential nodes in complex networks

Waseem Ahmad and Bang Wang

Link prediction in multiplex social networks: An information transmission approach

Lei Si, Longjie Li, Hongsheng Luo and Zhixin Ma

Cyclic symmetric dynamics in chaotic maps

Jin Liu, Kehui Sun and Huihai Wang

Relationship between micro-pores fractal characteristics about NMR T2 spectra and macro cracks fractal laws based on box dimension method of coal under impact load from energy dissipation theory

Shugang Li, Di He, Xiangguo Kong, Haifei Lin, Yankun Ma, Xuelong Li, Mengzhao Zhan, Pengfei Ji and Songrui Yang

Integral resonant negative derivative feedback suppression control strategy for nonlinear dynamic vibration behavior model

H.S. Bauomy, A.T. EL-Sayed and F.T. El-Bahrawy

Social contagion under hybrid interactions

Xincheng Shu, Man Yang, Zhongyuan Ruan and Qi Xuan

Cooperation dynamics of reputation-based manhattan distance social circle in spatial prisoner’s dilemma game in evolutionary game theory

Jinlong Ma and Hongfei Zhao

Penetrative convection in Navier–Stokes-Voigt fluid induced by internal heat source

Puneet Rana and Mahanthesh Basavarajappa

Dynamics analysis and adaptive neural network command filtering excitation control of stochastic power system

Jingxian Li, Ping Ma, Cong Wang, Shaohua Zhang and Hongli Zhang

Dynamical analysis and event-triggered neural backstepping control of two Duffing-type MEMS gyros with state constraints

Tingyao Hu, Shaohua Luo, Ya Zhang, Guangwei Deng and Hassen M. Ouakad

Emergence of relaxation beat-waves in genuinely nonlinear Klein-Gordon chain with bi-harmonic parametric excitation

Majdi Gzal, Victor Kislovsky and Yuli Starosvetsky

Fostering cooperative evolution through probabilistic punishment and environmental feedback in public goods game

Jiaqi Liu, Qianwei Zhang and Rui Tang

A novel global perspective: Characterizing the fractal basins of attraction and the level of chaos in a double pendulum

Bo Qin and Ying Zhang

LMI synchronization conditions for variable fractional-order one-sided Lipschitz chaotic systems with gain fluctuations

Liping Chen, Chuang Liu, António M. Lopes, Yong Lin, Yingxiao Liu and YangQuan Chen

Design of key term separated identification model for fractional input nonlinear output error systems: Auxiliary model based Runge Kutta optimization algorithm

Muhammad Aown Ali, Naveed Ishtiaq Chaudhary, Taimoor Ali Khan, Wei-Lung Mao, Chien-Chou Lin and Muhammad Asif Zahoor Raja

Dynamic analysis of viscoelastic functionally graded porous beams using an improved Bernstein polynomials algorithm

Yuhua Cui, Tao Zeng, Meiling Fan, Rina Wu, Guodong Xu, Xiaohong Wang and Jue Zhao

Evaluation of human epileptic brain networks by constructing simplicial complexes

Zhaohui Li, Xinyu Li, Mindi Li, Kexin Zhang, Xi Zhang and Xiaoxia Zhou

Non-similar investigation of magnetohydrodynamics hybrid nanofluid flow over a porous medium with Joule heating and radiative effects

Raheela Razzaq, Muhammad Nasir Abrar, Saiqa Sagheer and Umer Farooq

Three-dimensional m-HR neuron model and its application in medical image encryption

Qianqian Shi, Shaocheng Qu, Xinlei An, Ziming Wei and Chen Zhang

Construction of a deterministic mathematical model for the spatial-mass distribution of random fragments produced by cased charge explosion

Sheng Zhang, Zhen-Qing Wang, Shu-Tao Li, Ye-Qing Chen, Qing Zhu and Jia-Lin Chen

A special memristive diode-bridge-based hyperchaotic hyperjerk autonomous circuit with three positive Lyapunov exponents

Xianwei Rong, Jean Chamberlain Chedjou, Xiaoyan Yu, Makhkamov Bakhtiyor Shukhratovich, Donghua Jiang and Jacques Kengne

An adaptive exploration mechanism for Q-learning in spatial public goods games

Shaofei Shen, Xuejun Zhang, Aobo Xu and Taisen Duan

Einstein’s spacetime curvature and gravitational waves: Elucidating the gradient flow of scalar invariants, variations in the Ricci scalar, and gravitational wave propagation

Najeh Rekik and Bachir Ouari

A novel spatio-temporal prediction model of epidemic spread integrating cellular automata with agent-based modeling

Peipei Wang, Xinqi Zheng, Yuanming Chen and Yazhou Xu