Article
Mathematics, Interdisciplinary Applications
Sosthene Tsamene Tanekou, Janarthanan Ramadoss, Jacques Kengne, Germaine Djuidje Kenmoe, Karthikeyan Rajagopal
Summary: This article investigates a fourth-order autonomous dynamical system composed of a Duffing oscillator coupled to a van der Pol oscillator. The study reveals the existence of multiple bifurcation modes and the coexistence of periodicity, chaos, and hyperchaos in the coupled system. The impact of a fractional-order derivative is examined and PSpice simulations confirm the theoretical predictions.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Mathematics, Interdisciplinary Applications
Xujiong Ma, Jun Mou, Li Xiong, Santo Banerjee, Yinghong Cao, Jieyang Wang
Summary: This novel chaotic circuit system exhibits abundant dynamic behaviors and special phenomena, theoretical analysis and simulation results verify its potential applications in secure communication and image encryption.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Multidisciplinary
Chunlai Li, Zhen Chen, Xuanbing Yang, Shaobo He, Yongyan Yang, Jianrong Du
Summary: This paper investigates the self-reproducing dynamics in discrete-time system by constructing a two-dimensional map with infinitely many fixed points. Theoretical analysis and numerical simulations confirm that the attractor of the map can be non-destructively reproduced by initial values and parameters along all axis directions. Experimental measurements on a DSP-based platform validate the self-reproducing behavior of different types of attractors.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Ling Zhou, Zhenzhen You, Yun Tang
Summary: This paper introduces a new three-dimensional chaotic system that can generate different types of coexisting attractors with nested structures under fixed model parameters. The system exhibits sensitivity to initial conditions and can produce a multitude of coexisting attractors. The circuit implementation in Pspice supports numerical analyses and validates the mathematical model.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Multidisciplinary
R. Fangnon, Victor Kamdoum Tamba, C. H. Miwadinou, A. Monwanou, J. B. Chabi Orou
Summary: This study converts a two-dimensional modified Helmholtz oscillator into a three-dimensional modified Helmholtz jerk oscillator, and investigates the stability of fixed points as well as the bifurcation of Hopf using numerical simulations. The global dynamics and the coexistence of attractors are analyzed through the basin of parameters, attraction, bifurcation, Lyapunov exponents, and phase portrait. It is found that the modified Jerk Helmholtz oscillator can generate Hopf bifurcation, bistable limit cycles, and the coexistence of chaotic and periodic attractors under appropriate system parameter values. An experimental verification of the modified Jerk Helmholtz oscillator based on microcontroller implementation is proposed. Two new parameters are added to control the amplitude of the Lyapunov attractor and exponent in the modified Helmholtz jerk oscillator.
Article
Physics, Multidisciplinary
Sridevi Sriram, Adile Adoum Danao, Theophile Fozin Fonzin, Karthikeyan Rajagopal, Jacques Kengne
Summary: This study explores the dynamics of a pair of coupled inertial neurons with hyperbolic tangent activation function, revealing various nonlinear patterns and features such as coexisting bifurcation branches, merging crisis, and coexisting self-excited motions. Additionally, an analogue electronic circuit design is conducted to verify the diverse types of features reported during the theoretical study.
Article
Physics, Multidisciplinary
Qiao Wang, Zean Tian, Xianming Wu, Weijie Tan
Summary: A novel and simple Jerk chaotic circuit with three current feedback operational amplifiers included (CFOA-JCC) is proposed in this paper, which has a simpler circuit structure and fewer components but higher frequency characteristics. The dynamic behaviors of CFOA-JCC, such as equilibrium, stability, Lyapunov exponent, bifurcation diagram, offset boosting, and phase diagram, are analyzed. Furthermore, the frequency spectrum characteristic of CFOA-JCC is compared with that of the ordinary op-amps Jerk chaotic circuit, and the results show that CFOA-JCC has a much higher chaotic attractor frequency. Numerical simulation and hardware circuit experiments confirm the coexisting attractors of CFOA-JCC.
FRONTIERS IN PHYSICS
(2022)
Article
Mathematics
Ling Zhou, Zhenzhen You, Xiaolin Liang, Xiaowu Li
Summary: This paper investigates a simple memristor emulator consisting of a diode bridge and a capacitor, and demonstrates its pinched hysteresis loops and higher operating frequency. Through mathematical modeling, it is found that the system only possesses one unstable equilibrium point, and various bifurcations, periodic and chaotic orbits, and coexisting attractors are depicted.
Article
Multidisciplinary Sciences
Minxiu Yan, Jingfeng Jie, Ping Zhang
Summary: This study constructs a new chaotic system by changing the number of unknown parameters and investigates its dynamic behavior. It is found that the system undergoes complex changes when the number of same state variables in the nonlinear term varies. Moreover, the system maintains the chaotic attractor while the state of the attractor changes with the exponential change of a single-state variable. Experimental verification and application in image encryption systems show improved encryption and decryption characteristics.
SCIENTIFIC REPORTS
(2022)
Article
Mathematics, Interdisciplinary Applications
Sundarambal Balaraman, Jacques Kengne, M. S. Kamga Fogue, Karthikeyan Rajagopal
Summary: This article explores the dynamics of a ring of three unidirectional coupled excitation-free double well Duffing oscillators. The coupling technique used is the amplitude modulation of an oscillator with a proportion of the amplitude of its neighboring counterpart. The model's rate equation is a sixth-order autonomous nonlinear odd symmetric system with twenty-seven equilibrium points, eight of which undergo Hopf bifurcation. A detailed analysis of the model reveals fascinating dynamical features, including parallel bifurcation threes, Hopf bifurcations, and various types of coexisting modes of oscillations.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Engineering, Mechanical
Jingwei Wang, Yongxiang Zhang
Summary: Previous results suggest that some oscillators have a finite number of Wada basins. However, in this study, we discovered that a nonlinear oscillator can possess a countable infinity of connected Wada basins. The basin cell theorem and generalized basin cell theorem were used to investigate the infinite number of coexisting attractors and their Wada basins. These systematic Wada basins exhibit identical basin structures in each periodic X-axis coordinate interval, resulting in a high level of indeterminacy and extreme sensitivity to initial conditions.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Tao Ma, Jun Mou, Abdullah A. A. Al-Barakati, Hadi Jahanshahi, Shu Li
Summary: A new tri-cellular neural network system based on double memristors is constructed in this paper. Instead of the conventional segmentation function, a hyperbolic tangent function is used. The rich and complex dynamical characteristics of the system are presented through various analyses and experiments. The improved system provides a theoretical foundation in other fields of application, particularly for secure communications.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Koki Yoshida, Keiji Konishi, Naoyuki Hara
Summary: This study experimentally confirms the relationship between the unstable periodic orbit and the basin of the stabilized equilibrium point under delayed feedback control, providing useful insights for the design of delayed feedback controllers.
NONLINEAR DYNAMICS
(2021)
Article
Engineering, Electrical & Electronic
Leandre Kamdjeu Kengne, Justin Roger Mboupda Pone, Hilaire Bertrand Fotsin
Summary: The paper examines the dynamics of a memristive circuit with broken symmetry, using phase portraits, bifurcations, basins of attraction, and Lyapunov exponents to illustrate various nonlinear patterns. It is shown that perturbing the symmetry of the oscillator leads to more complex nonlinear phenomena, such as coexisting asymmetric bubbles of bifurcation and multiple asymmetric attractors, with PSpice simulation studies confirming the theoretical predictions.
INTERNATIONAL JOURNAL OF ELECTRONICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Yongxiang Zhang, Fanhui Zhang
Summary: We investigate the coexisting attractors and their Wada basins in a vibration isolation system under control parameters. The study shows that even though the attractors can be effectively controlled, Wada basins still exist, indicating a certain level of unpredictability in the system.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
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
Mathematics, Interdisciplinary Applications
V. R. Folifack Signing, G. A. Gakam Tegue, M. Kountchou, Z. T. Njitacke, N. Tsafack, J. D. D. Nkapkop, C. M. Lessouga Etoundi, J. Kengne
Summary: In this article, a chameleon cryptosystem based on a chameleon chaotic system and dynamic DNA coding is proposed for image encryption. The chosen chaotic sequences are tightly connected to disrupt the pixel image distribution. To enhance security, confusion and diffusion operations are closely related to the chaotic sequences. The experimental results demonstrate that the proposed cryptosystem performs well against various attacks.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
M. D. Vijayakumar, Hayder Natiq, Maxim Idriss Tametang Meli, Gervais Dolvis Leutcho, Zeric Tabekoueng Njitacke
Summary: This contribution introduces a novel memristive mega-stable oscillator (MMO) that exhibits mega-stability without external perturbation. The investigation of the oscillator's volume contraction rate reveals dissipative, conservative, and repelled dynamics depending on the bifurcation control parameter. The coexistence of attractors in a nested structure characterizes the mega-stability of the investigated oscillator. Multiple coexisting mega-stable attractors are supported by Pspice simulations.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Neurosciences
Zeric Tabekoueng Njitacke, Bernard Nzoko Koumetio, Balamurali Ramakrishnan, Gervais Dolvis Leutcho, Theophile Fonzin Fozin, Nestor Tsafack, Kartikeyan Rajagopal, Jacques Kengne
Summary: This paper investigates bidirectional-coupled neurons through an asymmetric electrical synapse, exploring different firing patterns under various electrical synaptic weights. It analyzes the equilibria, stabilities, and Hamiltonian energy of the model, as well as conducts Pspice simulations and digital implementation using an STM32F407ZE microcontroller development board to support the numerical results.
COGNITIVE NEURODYNAMICS
(2022)
Article
Physics, Multidisciplinary
Isaac Sami Doubla, Balamurali Ramakrishnan, Zeric Njitacke Tabekoueng, Jacques Kengne, Karthikeyan Rajagopal
Summary: This article studies a new model of Hopfield Neural Network (HNN) with two neurons and a hyperbolic-type memristor. The equilibrium points analysis shows that the system has an unstable line of equilibrium in the absence of external stimuli and no equilibrium point in the presence of external stimuli, indicating hidden attractors. Analyses for both cases reveal complex homogeneous and heterogeneous bifurcations with multiple coexisting attractors.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2022)
Article
Engineering, Mechanical
T. H. Tchinda, K. M. Wouapi, Z. Tabekoueng Njitacke, T. Fozin Fonzin, C. L. Gninzanlong, H. B. Fotsin
Summary: In this study, we investigate the dynamical behavior of a chaotic satellite system and demonstrate the occurrence of subcritical Hopf bifurcation as well as the coexistence of multiple orbits. We successfully apply a control strategy based on linear augmentation scheme to drive the satellite from chaotic orbit to periodic orbit.
JOURNAL OF VIBRATION ENGINEERING & TECHNOLOGIES
(2022)
Article
Mathematics, Interdisciplinary Applications
Zeric Tabekoueng Njitacke, Clovis Ntahkie Takembo, Jan Awrejcewicz, Henri Paul Ekobena Fouda, Jacques Kengne
Summary: This paper presents and studies the dynamics of a single neuron and a network of an improved FitzHugh-Nagumo model with memristive autapse. The investigation reveals hidden dynamics in the improved model, and the energy in the system is only affected by the strength of the memristive autapse. The study of the network with 500 neurons shows that it supports localized information patterns with synchronization as a means of information coding.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Mechanical
Zeric Tabekoueng Njitacke, Clovis Ntahkie Takembo, Bernard Nzoko Koumetio, Jan Awrejcewicz
Summary: This paper investigates an improved Wilson neuron model with a memristive autapse, revealing a variety of neuronal behaviors. The study suggests that high coupling has significant effects on chaotic and chimera-like behaviors in the network.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Electrical & Electronic
Zeric Tabekoueng Njitacke, Theophile Fonzin Fozin, Sishu Shankar Muni, Jan Awrejcewicz, Jacques Kengne
Summary: This study investigates the effects of memristive autapse on the dynamics of a 2D Hindmarsh-Rose neuron. The results show that the frequency of the external current has no impact on the energy, while the strength of the memristive autapse and the amplitude of the stimuli can influence the energy released by the neuron. The study reveals exotic neuronal behaviors such as reverse period doubling route to chaos, interior and exterior crises, and homogeneous extreme multistability.
AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS
(2022)
Article
Engineering, Electrical & Electronic
Zeric Tabekoueng Njitacke, Jan Awrejcewicz, Adelaide Nicole Kengnou Telem, Theophile Fonzin Fozin, Jacques Kengne
Summary: In this study, a new configuration involving the coupling of a 2D Fitzhugh-Nagumo (FN) neuron with a 3D Hindmarsh-Rose (HR) neuron via a memristive synapse is investigated. The self-excited dynamics of the coupled neurons is revealed after analyzing the equilibria of the model. Resting activity, periodic spikes, periodic and chaotic bursts are found during the numerical investigation of the model. The coupled neurons display the rare phenomenon of homogeneous extreme multistability, where an infinite number of firing activities of the same nature but located at different levels in the phase space coexist. The selection of desired electrical activity dynamics is also emphasized through a noninvasive control scheme. An electronic circuit of the coupled neuron is designed and investigated to support the obtained results.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2023)
Article
Physics, Multidisciplinary
Xi Zhang, Donghua Jiang, Jean De Dieu Nkapkop, Zeric Tabekoueng Njitacke, Musheer Ahmad, Liya Zhu, Nestor Tsafack
Summary: This paper investigates the dynamics of two different neurons coupled via memristive synapse and memristive autapse. The results suggest that the global dynamics of the system highly depends on the coupling strength. A cryptographic scheme based on both S-Box driven block compressive sensing and the memristive autapse synapse model is proposed, and performance analysis indicates that the coupling strength of the neural network model can be adjusted to increase or decrease the security of medical data.
Article
Physics, Multidisciplinary
Zeric Tabekoueng Njitacke, Sishu Shankar Muni, Soumyajit Seth, Jan Awrejcewicz, Jacques Kengne
Summary: This study focuses on the collective behavior of two HR neurons and a network of HR neurons. By connecting a traditional 3D HR neuron and a memristive 2D HR neuron through a gap junction, the collective behavior of the coupled neurons is obtained. Numerical simulations reveal that the coupled neurons exhibit various behaviors, including periodic, quasi-periodic, and chaotic bursting or spiking, by adjusting the control parameter. The network topology affects the spatiotemporal patterns, with cluster states observed in non-homogenous ring and star structures.
Article
Computer Science, Information Systems
Donghua Jiang, Zeric Tabekoueng Njitacke, Jean De Dieu Nkapkop, Nestor Tsafack, Xingyuan Wang, Jan Awrejcewicz
Summary: Wireless body area network (WBAN) is a crucial tool in modern medical areas for monitoring human vital signs. Security and bandwidth saturation are important challenges in WBAN technology. A neural network model called CRNN is analyzed and found to have self-excited dynamics. Experimental results show its application in medical image compression and security.
IEEE INTERNET OF THINGS JOURNAL
(2023)
Article
Automation & Control Systems
Zeric Tabekoueng Njitacke, Jean De Dieu Nkapkop, Vitrice Folifack Signing, Nestor Tsafack, Michael Ekonde Sone, Jan Awrejcewicz
Summary: This article explores the complex dynamics of a simple memristive tabu learning neuron (MTLN). The stability analysis reveals that the MTLN displays self-excited dynamics and is highly sensitive to initial conditions. The coexistence of an infinite number of chaotic attractors in the MTLN, which is a novel finding, represents an important contribution of this work. The chaotic dynamics of the MTLN are further applied to compress and encrypt digital medical images, achieving high compression/encryption performances with low computational cost.
IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS
(2023)
Article
Physics, Multidisciplinary
Janarthanan Ramadoss, Clovis Ntahkie Takembo, Anitha Karthikeyan, Zeric Tabekoueng Njitacke, Jan Awrejcewicz
Summary: This article studies the isolated and collective dynamics of a FitzHugh-Rinzel neuron by adding a third variable to the generic FitzHugh-Nagumo neural circuit. It investigates the stability around a zero time constant and reveals the hidden dynamics of the model. The energy is analytically and theoretically investigated to support the various firing activities captured in the model, and the collective behavior of a network made of 50 neurons is analyzed using modulation instability theory.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Mathematics, Interdisciplinary Applications
Bo Li, Tian Huang
Summary: This paper proposes an approximate optimal strategy based on a piecewise parameterization and optimization (PPAO) method for solving optimization problems in stochastic control systems. The method obtains a piecewise parameter control by solving first-order differential equations, which simplifies the control form and ensures a small model error.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Guram Mikaberidze, Sayantan Nag Chowdhury, Alan Hastings, Raissa M. D'Souza
Summary: This study explores the collective behavior of interacting entities, focusing on the co-evolution of diverse mobile agents in a heterogeneous environment network. Increasing agent density, introducing heterogeneity, and designing the network structure intelligently can promote agent cohesion.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Gengxiang Wang, Yang Liu, Caishan Liu
Summary: This investigation studies the impact behavior of a contact body in a fluidic environment. A dissipated coefficient is introduced to describe the energy dissipation caused by hydrodynamic forces. A new fluid damping factor is derived to depict the coupling between liquid and solid, as well as the coupling between solid and solid. A new coefficient of restitution (CoR) is proposed to determine the actual physical impact. A new contact force model with a fluid damping factor tailored for immersed collision events is proposed.
CHAOS SOLITONS & FRACTALS
(2024)
