Article
Mathematics, Interdisciplinary Applications
H. Bao, Y. Gu, Q. Xu, X. Zhang, B. Bao
Summary: This paper presents a novel parallel bi-memristor hyperchaotic map using the self-feedback method by connecting two identical discrete memristors in parallel. The map exhibits multistability and extreme multistability, and its dynamics depend on the memristor initial states.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Mechanical
Mo Chen, Xuefeng Luo, Yunhe Suo, Quan Xu, Huagan Wu
Summary: This work presents a memristor-coupled homogeneous network consisting of two identical non-autonomous memristive Fitzhugh-Nagumo models and investigates its coexisting and synchronous behaviors. The numerical results reveal coexisting hidden chaotic, periodic, and quasi-periodic attractors, and their synchronicities are controlled by the initial condition and coupling strength of the coupling memristor. In addition, phase synchronization is easily achieved due to the existence of external stimuli, and these synchronous states are flexibly controlled by the initial conditions.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Shaohui Yan, Yu Ren, Binxian Gu, Qiyu Wang, Ertong Wang
Summary: In this paper, a four-dimensional chaotic system based on a flux-controlled memristor with a cosine function is constructed. It has infinitely many equilibria. The distribution of infinitely many single-wing and double-wing attractors along the u-coordinate is obtained by changing the initial values of the system and keeping the parameters constant, verifying the initial-offset boosting behavior of the system. Additionally, the complex dynamical behavior of the system is studied in detail through various analysis techniques, and the proposed chaotic system is applied to image encryption and shows good security performance.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Physics, Multidisciplinary
Quan Xu, Tong Liu, Cheng-Tao Feng, Han Bao, Hua-Gan Wu, Bo-Cheng Bao
Summary: This paper introduces a continuous non-autonomous memristive Rulkov model, which reveals extreme multistability by considering the effects of electromagnetic induction and external stimulus. Numerical simulations and hardware experiments are conducted to verify the extreme multistability, broadening the future engineering applications of the Rulkov model.
Article
Engineering, Electrical & Electronic
Manuel Escudero, Sabina Spiga, Mauro Di Marco, Mauro Forti, Giacomo Innocenti, Alberto Tesi, Fernando Corinto, Stefano Brivio
Summary: This paper presents a framework for the physical implementation of a tunable memristor Chua's circuit and successfully generates different oscillation patterns by programming a nonvolatile memristive device to different states. The characterization and modeling of the real device were used to extend the experimental work and draw further requirements for successful circuit implementation.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
(2023)
Article
Mathematics, Interdisciplinary Applications
A. Othman Almatroud
Summary: In this paper, a simple fractional order discrete-time neural network with three neurons is introduced using the fractional I-Caputo operator. Experimentally investigated dynamics of this model show various types of coexisting attractors, as well as the interesting phenomena of extreme multistability, i.e. the coexistence of symmetric multiple attractors.
FRACTAL AND FRACTIONAL
(2021)
Article
Physics, Multidisciplinary
Xiaodong Jiao, Mingfeng Yuan, Jin Tao, Hao Sun, Qinglin Sun, Zengqiang Chen
Summary: In this paper, a new five-dimensional double-memristor hyperchaotic system is introduced and its boundness condition is proved. Simulation results reveal the existence of transient hyperchaos and hidden extreme multistability in the system, and the generated signal sequence is shown to be highly random for encryption purposes. Furthermore, the system is implemented on an FPGA experimental platform, facilitating further applications of the proposed hyperchaos.
Article
Mathematics
Jiang Wang, Yang Gu, Kang Rong, Quan Xu, Xi Zhang
Summary: This article proposes a new discrete memristor-based Lozi map that can generate hidden hyperchaos. The dynamical effects of the discrete memristor on the map and the existence of hidden attractors are demonstrated.
Article
Engineering, Mechanical
Chunlai Li, Yongyan Yang, Xuanbing Yang, Xiangyu Zi, Fanlong Xiao
Summary: This paper introduces a nonvolatile locally active memristor with three stable equilibrium states for three-bit-per-cell memory device functionality. A neural network model composed of three Hopfield neurons is presented, showing that the distribution of system equilibrium points depends on the coupling weight of the memristor synapse. The bifurcation diagram reveals the coexistence phenomenon of multiple stable modes, with complex bursting oscillation emerging in the neural network when there is a step difference between the system's natural frequency and the external excitation frequency.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Bocheng Bao, Jingting Hu, Jianming Cai, Xi Zhang, Han Bao
Summary: This paper constructs a memristor-based neuron model and investigates the memristor effect in a discrete map as well as its impact on neuronal behavior. Numerical methods reveal complex mode transition behaviors, which are strongly dependent on the initial state of the memristor. Furthermore, a hardware platform is developed to demonstrate the effectiveness of the memristive neuron model in imitating firing activities of biological neurons.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Electrical & Electronic
Isaac Sami Doubla, Balamurali Ramakrishnan, Zeric Tabekoueng Njitacke, Jacques Kengne, Karthikeyan Rajagopal
Summary: This article investigates a single nonautonomous Hopfield neuron that uses a new hyperbolictype memristor for self-synaptic weight. The analysis of the model reveals various nonlinear phenomena, such as the coexistence of symmetric bifurcation diagrams and multiple periodic hidden attractors and chaotic hidden attractors. The study also successfully demonstrates the control of multiple coexisting hidden chaotic attractors in specific conditions.
AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS
(2022)
Article
Engineering, Mechanical
Chuanhong Du, Licai Liu, Zhengping Zhang, Shixing Yu
Summary: By coupling two memristors, a method for constructing a high-dimensional memristive chaotic system is proposed, resulting in a five-dimensional chaotic system with double memristors. The system exhibits extreme transient behaviors, including various transitions and extreme multistability when changing initial conditions, validated using the spectral entropy algorithm.
NONLINEAR DYNAMICS
(2021)
Article
Engineering, Mechanical
Mei Guo, Ran Yang, Meng Zhang, Renyuan Liu, Yongliang Zhu, Gang Dou
Summary: A novel memcapacitor designed with SBT memristor and two capacitors is proposed in this paper, along with a fifth-order memcapacitor and memristor chaotic circuit. The dynamic behaviors and stability of the system are analyzed, revealing various dynamic phenomena under different initial values and parameters. The study expands the research methods of memcapacitor for chaotic circuits.
NONLINEAR DYNAMICS
(2021)
Article
Physics, Applied
Xiaoxia Li, Chi Zheng, Xue Wang, Yingzi Cao, Guizhi Xu
Summary: This paper introduces a new four-dimensional chaotic system with symmetric coexisting bifurcation behaviors and four coexisting attractors. By replacing the coupling resistor, a four-dimensional memristive chaotic system is constructed, showing extreme multistability phenomenon. The dynamics of the systems are fully analyzed using phase portraits, Lyapunov exponent spectra, and coexisting bifurcation diagrams.
MODERN PHYSICS LETTERS B
(2021)
Article
Physics, Multidisciplinary
Shaohui Yan, Defeng Jiang, Hanbing Zhang, Yuyan Zhang, Yu Cui, Lin Li
Summary: This paper introduces memristor into a chaotic system to enrich its dynamic behaviors. The proposed system exhibits a wide range of dynamic behaviors, such as changing equilibrium point type, transient chaos, offset-boosting, and a special type of extreme multistability. The system is also successfully applied in an encryption system, which demonstrates good security and resistance against various attacks.
Article
Mathematics, Applied
Piyush P. Singh, Manashita Borah, Asim Datta, Sajad Jafari, Binoy K. Roy
Summary: Chaotic states of abnormal vasospasms in blood vessels increase the vulnerability of heart patients to severe COVID-19 infections, leading to high mortality rates. This paper introduces a model called the N-type blood vessel model (NBVM) to understand the dynamics of abrupt vasospasms under uncertainties. Active-adaptive controllers are used to synchronize the chaotic turbulence responsible for undesirable fluctuations in blood vessel diameter and pressure. The fractional-order NBVM exhibits rich dynamics and faster adaptive synchronization compared to its integer order model. The practical implications of this study lie in analyzing chaotic dysfunctionalities of blood vessels and developing control strategies for COVID-19-induced heart diseases.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2023)
Article
Mathematics, Applied
Zahra Dayani, Fatemeh Parastesh, Fahimeh Nazarimehr, Karthikeyan Rajagopal, Sajad Jafari, Eckehard Schoell, Juergen Kurths
Summary: In this paper, a time-varying coupling function is proposed to enhance synchronization in complex networks of oscillators. The stability of synchronization is analyzed using the master stability approach, considering the largest Lyapunov exponent of the linearized variational equations as the master stability function dependent on the network eigenvalues. Diffusive single-variable coupling is assumed for the oscillators, and the coupling with the smallest local Lyapunov exponent is selected for each time interval. The obtained coupling function decreases the critical coupling parameter, leading to enhanced synchronization. Moreover, it achieves faster synchronization and increased robustness. Illustratively, the optimal coupling function is found for three networks of chaotic Rossler, Chen, and Chua systems, showing enhanced synchronization.
Article
Mathematics, Applied
Fatemeh Parastesh, Sridevi Sriram, Hayder Natiq, Karthikeyan Rajagopal, Sajad Jafari
Summary: This paper proposes an optimization algorithm based on the eigenvalues of the connectivity matrix to construct a network with optimal synchronization. The proposed algorithm shows better synchronization ability compared to random link addition and a method based on eigenvector centrality. It also performs well in preserving synchronization in scale-free and small-world networks with the same number of nodes and links. Additionally, the algorithm is effective for link reduction while maintaining synchronization.
Review
Mathematics, Interdisciplinary Applications
Zhen Wang, Atefeh Ahmadi, Huaigu Tian, Sajad Jafari, Guanrong Chen
Summary: This paper provides a brief review of lower-dimensional chaotic systems with unusual complex characteristics, serving as a handy reference for future research on chaotic systems.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Atiyeh Bayani, Sajad Jafari, Hamed Azarnoush, Fahimeh Nazarimehr, Stefano Boccaletti, Matjaz Perc
Summary: Transitions from incoherent to coherent dynamical states can be observed in various real-world networks, and they can be explosive or continuous. The nature of the transition changes depending on the initial conditions, and the critical coupling strength for explosive synchronization also depends on the initial conditions.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Shilpa Garai, Sarbari Karmakar, Sajad Jafari, Nikhil Pal
Summary: In biological control programs, providing additional food for predators can distract them from overconsumption of prey in the short term or enhance predation rate in the long term. This study explores the impact of additional food on prey growth and overall system dynamics in a predator-prey model. The researchers analyze system dynamics by varying two control parameters and observe rich and complex dynamical behaviors, including structurally stable periodic patterns and the presence of organized periodic structures. The study also reveals the coexistence of different types of attractors, including triple and quadruple attractors, which is a rare phenomenon in ecological systems.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Mahtab Mehrabbeik, Sajad Jafari, Riccardo Meucci, Matjaz Perc
Summary: This paper studies the synchronization of globally coupled identical laser models via linear and nonlinear forms of diffusive couplings. The results show that complete synchronization can be achieved in laser models under linear diffusive function but not under nonlinear diffusive function. Multistability is observed in different network states such as cluster synchronization, chimera, and solitary states.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Physics, Multidisciplinary
Atefeh Ahmadi, Sriram Parthasarathy, Hayder Natiq, Karthikeyan Rajagopal, Guillermo Huerta-Cuellar, Sajad Jafari
Summary: This paper investigates the classical Lorenz model with a periodic heating term replacing the constant one. The application of a variable heating term results in time-dependent behaviors in the Lorenz model. The produced time series are chaotic but exhibit fixed points or periodic-like qualities in certain intervals. The study comprehensively examines energy dissipation, equilibrium points, and demonstrates that the modified Lorenz system is a multi-stable system capable of demonstrating multiple coexisting attractors by changing its initial conditions.
Article
Multidisciplinary Sciences
Atefeh Ahmadi, Sourav Roy, Mahtab Mehrabbeik, Dibakar Ghosh, Sajad Jafari, Matjaz Perc
Summary: This paragraph discusses the duopoly Stackelberg model in game theory, where a leader and a follower firm compete in the market to maximize profit. Real-world markets can exhibit chaotic behaviors and unpredictable changes. Taking into account the heterogeneity of the firms, a Stackelberg model with heterogeneous players and marginal costs is proposed. The equilibrium points, including the Nash equilibrium, are calculated and their stability is analyzed. Different parameters are explored to understand the dynamics through bifurcation diagrams, Lyapunov exponents spectra, and Kaplan-Yorke dimension. By combining state feedback and parameter adjustment methods, the chaotic solutions of the model are tamed and it converges to the Nash equilibrium.
Article
Physics, Multidisciplinary
Nastaran Navid Moghadam, Ramesh Ramamoorthy, Fahimeh Nazarimehr, Karthikeyan Rajagopal, Sajad Jafari
Summary: Several mathematical models have been proposed to explain neural behaviors in networks. This study examines the bifurcation points of the attention-deficit disorder model in regular and irregular networks. Results show that recovery time of disturbed neurons reveals the dynamical variation of the nodes. Additionally, as coupling strengths and nodes' degree increase, bifurcations occur in smaller parameters in the period-doubling route to chaos, but no general trend is observed in the inverse route of period doubling.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Physics, Multidisciplinary
Dorsa Nezhad Hajian, Gayathri Vivekanandhan, Hayder Natiq, Fatemeh Parastesh, Karthikeyan Rajagopal, Safari Jafari
Summary: This paper investigates the complete synchronizability of coupled periodically forced chaotic systems using the master stability function method. Three classic chaotic systems are employed for this study, and numerical simulations supporting the findings are reported. The results suggest that chaotic forced systems tend to synchronize at weaker couplings than the autonomous versions with increased stimulation, while high-frequency stimulation is completely ineffective. The required forcing amplitude also depends on the system's attractor size.
Article
Engineering, Electrical & Electronic
Yicheng Jiang, Chunbiao Li, Chuang Zhang, Tengfei Lei, Sajad Jafari
Summary: By introducing a mathematical meminductor into a jerk system, the same oscillation can be achieved. Therefore, a new structure dominated by a meminductor can be used to realize the system.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2023)
Article
Physics, Multidisciplinary
Fatemeh Parastesh, Zahra Dayani, Alireza Bahramian, Sajad Jafari, Guanrong Chen
Summary: This paper investigates the conventional PID control method for synchronizing a network of chaotic systems. The approach uses the master stability function and hyperjerk systems to overcome difficulties in calculating integral and derivative couplings. It is found that the most efficient coupling for network synchronization is the proportional-integral coupling.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2023)
Article
Physics, Multidisciplinary
Gayathri Vivekanandhan, Hayder Natiq, Aboozar Ghaffari, Atiyeh Bayani, Karthikeyan Rajagopal, Sajad Jafari
Summary: This paper presents a chaotic jerk oscillator with a heart-shaped attractor and the coexistence of chaotic and periodic attractors. The analysis of bifurcation diagram, Lyapunov exponent, and basin of attraction confirms the chaotic and periodic properties of the oscillator.
Article
Physics, Multidisciplinary
Balamurali Ramakrishnan, Hayder Natiq, Ahmed M. Ali Ali, Karthikeyan Rajagopal, Fahimeh Nazarimehr, Sajad Jafari
Summary: This paper presents a mathematical model for examining the hemostatic behaviors of neural activity and extracellular matrix (ECM) molecules. The dynamic behaviors of the proposed model are investigated using tools such as Lyapunov exponents and bifurcation diagrams. The coexistence of periodic and chaotic dynamics in ECM is demonstrated, which is believed to be distinct modulation modes of neuronal circuits. Additionally, the synchronization characteristics of the coupled systems are examined using the master stability function, showing that certain coupling configurations can synchronize the models. This research is significant for neurologists to understand brain rhythms and their roles.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
