Article
Mathematics, Interdisciplinary Applications
Nzoulewa Dountsop Sandrine, Kengne Jacques
Summary: In recent years, research on chaotic models with cyclic connection of variables has been extensively conducted, focusing on their specific features such as multistability and amplitude control. Models with ring connection of variables have shown a coexistence of up to twelve disconnected attractors. This study presents a quintic chaotic model with cyclic connection of variables, emphasizing its complexity and potential applications in the engineering domain. The study demonstrates the phenomenon of offset boosting by introducing four constants, and reveals multistability with the coexistence of eight and sixteen attractors using phase portraits. Nonlinear dynamical tools are used to investigate the system's dynamics and highlight important phenomena. The numerical results are confirmed using PSpice, showing a double-band chaotic attractor. Additionally, total amplitude control is achieved, demonstrating the oscillator's potential as an attenuator or amplifier in the engineering domain. The method of adaptive synchronization is applied to emphasize its implications in secure communication systems.
Article
Mathematics, Interdisciplinary Applications
Chengwei Dong
Summary: This paper investigates the fundamental dynamics of a novel three-dimensional chaotic system with hidden attractors and coexisting attractors, and demonstrates its potential in engineering applications.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Xinyu Li, Chunlei Fan, Jian Zeng, Qun Ding
Summary: This paper proposes a novel 4D conservative chaotic system and analyzes its dynamic behaviors. The system is found to have hidden attractors and conservative characteristics, exhibiting various special behaviors. Complexity analysis shows a significant improvement in sequence complexity compared to existing systems. This research lays the foundation for subsequent engineering applications.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Engineering, Mechanical
Qiyu Wang, Shaohui Yan, Ertong Wang, Yu Ren, Xi Sun
Summary: A simple four-dimensional chaotic system is proposed in this paper, which is considered as a Hamiltonian conservative system based on the analysis of Hamiltonian energy and conservative nature. The conservative and chaotic properties of the system are verified through phase diagram, Lyapunov exponents, bifurcation diagram, and complexity diagram. The extreme multistability of the system is studied, showing the coexistence of unequal and equal energy levels. The topology of these conservative motions is closely related to the isoenergy line of the Hamiltonian function. Additionally, the offset-boosting under parameter control is investigated, and the feasibility of the system is verified through simulation and experimental circuits. Furthermore, the system is applied to finite-time synchronization, laying a foundation for practical engineering applications.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Chenguang Ma, Jun Mou, Li Xiong, Santo Banerjee, Tianming Liu, Xintong Han
Summary: This paper presents a new four-dimensional dissipative chaotic system capable of producing multiple asymmetric attractors, with analysis on its dynamical behavior. The system exhibits asymmetric multistability in the basin of attraction, and different types of asymmetric coexisting attractors are observed with changes in bifurcation parameters. The spectral entropy complexity chaotic diagrams are used to observe changes in sequence complexity as bifurcation parameters change simultaneously.
NONLINEAR DYNAMICS
(2021)
Article
Physics, Applied
Lingyun Li, Degui Kong, Zhijun Chai, Yunxia Wang
Summary: In this paper, a novel four-wing chaotic system based on the Sprott-A system is constructed. The system contains three nonlinearly quadratic terms, showing rich dynamics including four-wing hidden attractors, hidden extreme multistability, and transient transitions. Spectral entropy analysis confirms its high complexity. A corresponding hardware analog circuit is designed and confirmed to be practically feasible. This system has promising application value in secure communication and cryptography.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Physics, Multidisciplinary
Li-Li Jia, Bang-Cheng Lai
Summary: This article introduces a new memristive chaotic system and highlights its ability to generate multiple stable states and control the amplitude.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Physics, Multidisciplinary
Xiefu Zhang, Zean Tian, Jian Li, Xianming Wu, Zhongwei Cui
Summary: This study investigates a hidden chaotic system without equilibrium point using various numerical methods, identifying seven types of attractors and some interesting characteristics through analysis. The Spectral Entropy algorithm is applied for system analysis, and physical implementation is conducted to verify its feasibility.
Article
Computer Science, Information Systems
Junjie Wen, Yiran Feng, Xueheng Tao, Yinghong Cao
Summary: This paper introduces a new 5-D chaotic system with hidden attractor, analyzing its stability and special phenomena, verifying its engineering applications, and proposing an offset boosting control method. By numerical simulation and analyzing the complexity of SE and C-0, as well as simulating the system using DSP technology, the results align well with the numerical simulation results. Theoretical analysis and simulation show the system's complex dynamical characteristics for secure communication and image encryption applications.
Article
Mathematics, Applied
Shaohui Yan, Ertong Wang, Qiyu Wang
Summary: A new fractional-order chaotic system is constructed based on the Sprott system, which exhibits chaotic properties without equilibrium points. The system shows intermittent chaotic phenomena and multistability by changing parameters and order, as well as different initial values.
Article
Mathematics, Interdisciplinary Applications
Chenyang Hu, Qiao Wang, Xiefu Zhang, Zean Tian, Xianming Wu
Summary: In this paper, a three-dimensional nonlinear system with remarkable dynamical behavior is constructed based on the Anishchenko-Astakhov oscillator. By tuning only one parameter, the system exhibits various shapes of attractors and multiple types of dynamical behavior. The system shows multistability and transient behavior, increasing the complexity of the system.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Multidisciplinary Sciences
Naveed Khan, Zubair Ahmad, Jamal Shah, Saqib Murtaza, M. Daher Albalwi, Hijaz Ahmad, Jamel Baili, Shao-Wen Yao
Summary: In this paper, the dynamics of a chaotic system based on a circuit design is analyzed using the newly developed Fractal-Fractional derivative with power law kernel. The problem is modeled using classical order nonlinear, coupled ordinary differential equations, which are then generalized through Fractal-Fractional derivative with power law kernel. The theoretical analyses such as model equilibria, existence, uniqueness, and Ulam stability of the system have been calculated. A numerical technique using MATLAB software is used to analyze the highly non-linear fractal-fractional order system. The graphical solutions are presented in two dimensional graphs and three dimensional phase portraits and discussed in detail, with some concluding remarks drawn from the study. It is worth noting that fractal-fractional differential operators can quickly converge the dynamics of a chaotic system to its static equilibrium by adjusting the fractal and fractional parameters.
SCIENTIFIC REPORTS
(2023)
Article
Physics, Multidisciplinary
Qiqi Peng, Shuangquan Gu, Xiangxin Leng, Baoxiang Du
Summary: In this paper, a new four-dimensional incommensurate fractional-order system is proposed by introducing an ideal flux-controlled memristor into a three-dimensional chaotic system, and combining it with fractional-order calculus theory. The system is solved using the Adomian decomposition method and exhibits rich dynamical behaviors, such as antimonotonicity, transient transition behaviors, initial offset boosting behavior, hidden extreme multistability, and generation of various attractors as the order changes. Numerical simulations and hardware circuit implementation validate the analysis and physical realizability of the system.
Article
Mathematics, Interdisciplinary Applications
Abdul-Basset A. Al-Hussein, Fadhil Rahma Tahir, Karthikeyan Rajagopal
Summary: This study explores the nonlinear dynamics of an incommensurate fractional-order SMIB power system using modern nonlinear analysis theories like bifurcation, chaos, PSD, and bicoherence. The research shows that the system exhibits interesting dynamics such as periodic motion, chaotic oscillations, and multistability within specific parameter ranges. A novel linear augmentation-based control scheme is proposed to dampen chaotic oscillations, change stability, and transition the system from multistability to monostability, with Lyapunov theory used to derive the control system's stability. Simulation results confirm the effectiveness and robustness of the proposed control scheme in damping power system oscillations and improving overall performance.
Article
Mathematics, Interdisciplinary Applications
Atefeh Ahmadi, Sriram Parthasarathy, Hayder Natiq, Sajad Jafari, Igor Franovic, Karthikeyan Rajagopal
Summary: This paper introduces the first three-dimensional non-autonomous chaotic system that displays both megastability and extreme multistability, jointly called mega-extreme multistability. Different types of coexisting attractors are characterized by phase portraits, first return maps, bifurcation diagrams, Lyapunov spectra, Kaplan-Yorke dimension, connecting curves, and basins of attraction. The dissipative nature of the system is demonstrated, and the feasibility and applicability of the model are shown through analog circuit simulation.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Optics
Balakrishnan Sriram, Aboozar Ghaffari, Karthikeyan Rajagopal, Sajad Jafari, Esteban Tlelo-Cuautle
Summary: In this study, a chaotic map consisting of two sine functions is investigated to understand its chaotic dynamics. Bifurcation diagrams and Lyapunov exponents of the map reveal the presence of multistability in certain intervals of the bifurcation parameter. Furthermore, an encryption method based on sparse representation and the chaotic map is proposed. The experimental results showcase the improved image reconstruction performance and security level of this method compared to previous approaches.
Article
Physics, Multidisciplinary
Janarthanan Ramadoss, Hayder Natiq, Fahimeh Nazarimehr, Shaobo He, Karthikeyan Rajagopal, Sajad Jafari
Summary: This paper proposes the behavior of a 1D chaotic map that includes two sine terms and shows unique dynamics. By varying the bifurcation parameter, the map generates a shift and the system's dynamics are generated around the cross points of the map and the identity line. The irrational frequency of the sine term results in stable fixed points in some parameter intervals by increasing the bifurcation parameter. The proposed system, known as multistable, achieves multiple steady states in some intervals of the parameter, and the multistability dynamics are investigated using cobweb diagrams that reveal an interesting asymmetry in repeating parts of the bifurcation diagram.
Article
Physics, Multidisciplinary
Janarthanan Ramadoss, Adelaide Nicole Kengnou Telem, Jacques Kengne, Karthikeyan Rajagopal
Summary: This work proposes a new chaotic jerk system with septic nonlinearity and investigates its characteristics and behaviors. The most interesting feature discovered is the occurrence of up to eight coexisting attractors for appropriate sets of parameters. Multistability control is achieved through the linear augmentation approach, and the coupling breaks the symmetry of the system, inducing new patterns. PSPICE simulation results are consistent with the theoretical investigations.
Article
Physics, Multidisciplinary
Balamurali Ramakrishnan, Victor Kamdoum Tamba, Justin Roger Mboupda Pone, Serge Gervais Mbouna Ngueuteu, Karthikeyan Rajagopal
Summary: This paper presents a report on the microcontroller implementation of an autonomous three-dimensional oscillator with five terms (ATDOFT) and performance analysis based on partial and total amplitude controls. The ATDOFT displays periodic spiking behaviors, chaotic states, coexisting attractors, and bistable attractors. The study reveals that the spiking oscillations in the ATDOFT arise from the system switching between the unstable state and the stable state of the lone equilibrium point of the fast subsystem. Total and partial amplitude controls are achieved by inserting two controller parameters into the rate equations of the ATDOFT. The dynamical behaviors found in ATDOFT are validated by the microcontroller implementation.
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
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
Mathematics
Mahtab Mehrabbeik, Atefeh Ahmadi, Fatemeh Bakouie, Amir Homayoun Jafari, Sajad Jafari, Dibakar Ghosh
Summary: In network analysis, pairwise connections often overlook the higher-order connections among network nodes. However, these higher-order connections become more important in neuronal network synchronization, where simplicial complexes can represent non-pairwise connections. Map-based models offer a solution by reducing computational costs and increasing efficiency. This paper investigates the impact of pairwise and non-pairwise neuronal interactions on synchronization using memristive Hindmarsh-Rose neuron maps, showing that neurons can achieve synchrony with weak coupling strengths through chemical pairwise and non-pairwise synapses.
Article
Mathematics, Applied
Gervais Dolvis Leutcho, Lyne Woodward, Francois Blanchard
Summary: This paper investigates the dynamic behaviors of nonlinear metasurfaces in the terahertz frequency range using numerical methods. It shows the existence of periodic and chaotic modes and explores the coexistence of two stable states. The study of multistability represents an important step towards developing photonic memory devices in the THz frequency range.
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
Mathematics, Interdisciplinary Applications
Gayathri Vivekanandhan, Mahtab Mehrabbeik, Hayder Natiq, Nikhil Pal, Karthikeyan Rajagopal, Sajad Jafari
Summary: This paper investigates the contribution of basal ganglia regions in absence seizures and provides a detailed analysis of the basal ganglia cortex-thalamus (BGCT) model. The study finds that the BGCT model can exhibit chaotic behavior in small regions of the coupling parameter.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Mathematics, Interdisciplinary Applications
Sridevi Sriram, Hayder Natiq, Karthikeyan Rajagopal, Fatemeh Parastesh, Sajad Jafari
Summary: Consolidation of new information in memory during sleep involves the simultaneous occurrence of sharp-wave ripples (SWR) in the hippocampus, fast-slow spindles in the thalamus, and up and down oscillations in the cortex. This study investigates the effect of synaptic connections between neurons in the hippocampus, cortex, and thalamus networks on the formation of SWR and spindles. The results suggest that synaptic self-connection and inhibitory synaptic connection of excitatory neurons in the CA3 region of the hippocampus, as well as synaptic connection between CA1 excitatory neurons and cortex neurons, have the most significant influence on the network's dynamic behavior.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
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)
Article
Mathematical & Computational Biology
Gayathri Vivekanandhan, Mahtab Mehrabbeik, Karthikeyan Rajagopal, Sajad Jafari, Stephen G. Lomber, Yaser Merrikhi
Summary: A recent study found that the dimensionality of spiking activity in the middle temporal (MT) cortex increases after spatial working memory deployment. This study aims to analyze the ability of nonlinear and classical features to capture the content of working memory from MT neurons' spiking activity. The results suggest that only the Higuchi fractal dimension can be considered as a unique indicator of working memory, while other features like Margaos-Sun fractal dimension, Shannon entropy, corrected conditional entropy, and skewness may indicate other cognitive factors.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Mathematical & Computational Biology
Gayathri Vivekanandhan, Hamid Reza Abdolmohammadi, Hayder Natiq, Karthikeyan Rajagopal, Sajad Jafari, Hamidreza Namazi
Summary: This paper introduces the fractional order discrete Rulkov neuron map and analyzes its dynamics and synchronization ability. The results show that increasing the order of the fractional order decreases the stable areas of the system, and the fractional order systems cannot achieve complete synchronization.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Physics, Multidisciplinary
Tinggui Chen, Baizhan Xia, Dejie Yu, Chuanxing Bi
Summary: This study proposes a gradient phononic crystal structure for enhanced acoustic sensing. By breaking the symmetry of the PC structure, topologically protected edge states are introduced, resulting in topological acoustic rainbow trapping. The robustness and enhancement properties are verified numerically and experimentally.
