Article
Engineering, Mechanical
Karthikeyan Rajagopal, Irene Moroz, Balamurali Ramakrishnan, Anitha Karthikeyn, Prakash Duraisamy
Summary: The study investigated the effects of electric and magnetic fields on neurons, showing that exposure to both fields can significantly impact neurons, leading to complex oscillations. In network models, nodes exposed to both electric and magnetic fields exhibit more stable spiral waves compared to nodes exposed only to magnetic fields, and increasing the number of network layers increases the range of electric field frequencies for which spiral waves are formed.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Karthikeyan Rajagopal, Sajad Jafari, Chunbiao Li, Anitha Karthikeyan, Prakash Duraisamy
Summary: The introduction of magnetic flux coupling in neuron models has shown to suppress spiral waves in networks, while considering delayed asymmetric electrical synapse coupling is more effective at suppressing spiral waves compared to magnetic flux coupling.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Karthikeyan Rajagopal, Shirin Panahi, Mo Chen, Sajad Jafari, Bocheng Bao
Summary: The paper presents a fractional-order 1D neuron map and analyzes its dynamical characteristics through bifurcation diagrams and Lyapunov exponents' diagram. In a 2D lattice, the emergence of spiral wave as a significant collective behavior is studied, along with the examination of the effects of changing stimuli and parameters in the network. Additionally, an effective method of suppressing the spiral wave through impulse triggering has been investigated.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics
Janarthanan Ramadoss, Asma Alharbi, Karthikeyan Rajagopal, Salah Boulaaras
Summary: We discuss the dynamics of a fractional order discrete neuron model with electromagnetic flux coupling. The bifurcation dynamics of the fractional order neuron map show an inverse period-doubling route to chaos as a function of control parameters. We present a two-parameter phase diagram using the Lyapunov exponent to categorize the various dynamics present in the system. In addition, we explore the network behavior of the fractional order neuron map and investigate the impact of various parameters on wave propagation.
ELECTRONIC RESEARCH ARCHIVE
(2022)
Article
Mathematics, Interdisciplinary Applications
Bo Yan, Fatemeh Parastesh, Shaobo He, Karthikeyan Rajagopal, Sajad Jafari, Matjaz Perc
Summary: This study investigates synchronization in multiplex neuronal networks composed of fractional-order Hindmarsh-Rose neurons and finds that fractional-order models achieve better synchronization compared to integer-order models. By reducing the derivative order of the model, the required coupling strengths for interlayer or intralayer synchronization can be weakened, and the dependence of synchronization on coupling strength decreases.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Interdisciplinary Applications
Dan Liu, Song Zhao, Xiaoyuan Luo, Yi Yuan
Summary: The study focuses on the generalized projective synchronization problem of fractional-order extended Hindmarsh-Rose neuronal models with magneto-acoustical stimulation input. An NN sliding mode algorithm is derived to achieve synchronous control of neurons, allowing the master-slave neuron system to achieve GPS in a finite amount of time and exhibit resilience towards uncertain parameters and external disturbances.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Dawei Ding, Xiaoyu Chen, Zongli Yang, Yongbing Hu, Mouyuan Wang, Hongwei Zhang, Xu Zhang
Summary: In this study, the dynamics of fractional-order memristor-coupled Hindmarsh-Rose neuron model considering synaptic crosstalk were investigated. The qualitative analysis revealed the equilibrium points and stability, showing that the number and stability of equilibrium points varied with different crosstalk strength parameters. The phase diagrams, Lyapunov exponent spectrums, and bifurcation diagrams demonstrated the global coexistence of multiple firing patterns and the local attraction basins. The two-parameter bifurcation diagram described the parameter-related firing behaviors. Spectral entropy and C0 complexity chaos diagram were used to observe the change of system complexity when two parameters changed simultaneously. The digital implementations based on ARM were conducted to verify the consistency with the numerical simulation results.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Xinlei An, Shuai Qiao
Summary: This paper investigates the discharge patterns of a HR neuron under electromagnetic induction, including hidden, period-adding, mixed-mode oscillations, and their control methods. Theoretical analysis and numerical simulations are combined to study the equilibrium points and stability in the system, as well as the existence of Hopf bifurcation points. The results provide insights into understanding discharge patterns and controlling membrane voltage transfer in the magnetic flux HR neuron system.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Neurosciences
Karthikeyan Rajagopal, Janarthanan Ramadoss, Shaobo He, Prakash Duraisamy, Anitha Karthikeyan
Summary: This article discusses various dynamical properties of a four-dimensional mammalian cold receptor model, focusing on the effects of noise and temperature on collective behavior. By introducing obstacles in the network, the study shows how they affect wave reentry and proposes a new technique to identify it using individual node periods.
COGNITIVE NEURODYNAMICS
(2023)
Article
Neurosciences
Shaobo He, Karthikeyan Rajagopal, Anitha Karthikeyan, Ashokkumar Srinivasan
Summary: This study proposes a new discrete neuron model derived from the Huber-Braun neuron, which introduces additional slow and subthreshold currents and temperature dependent ion channels to study the firing pattern of neurons. Bifurcation, Lyapunov exponents, and sample entropy algorithm are used to analyze the dynamical behaviors of the model. The spatiotemporal behavior of the discrete neuron model is investigated in both single- and two-layer networks, and the induction of spiral waves in the network is studied.
COGNITIVE NEURODYNAMICS
(2023)
Article
Physics, Applied
Lixin Yang, Peiyan He, Jie Ma, Gaihui Guo
Summary: This paper focuses on the dynamic analysis of the magnetic flux e-HR neuron model with time delays, revealing that the system exhibits Hopf bifurcation within a specific range of time delay and increasing time delay can induce tip discharge behavior.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2022)
Article
Neurosciences
Haiying Li, Xiang Li, Zhongmou Xu, Jinxin Lu, Chang Cao, Wanchun You, Zhengquan Yu, Haitao Shen, Gang Chen
Summary: This study reveals the dual role of autophagy in cerebral ischemia-reperfusion injury and highlights the potential of targeting specific proteins associated with autophagy for improving the prognosis of ischemic stroke.
JOURNAL OF NEUROSCIENCE
(2022)
Article
Mathematics, Interdisciplinary Applications
Balamurali Ramakrishnan, Fatemeh Parastesh, Sajad Jafari, Karthikeyan Rajagopal, Gani Stamov, Ivanka Stamova
Summary: This paper investigates synchronization problems in a multiple network of Caputo-Fabrizio type fractional order neurons with different derivative orders in each layer. It is found that lower fractional orders result in intralayer synchronization and decreased interlayer coupling strength needed for near synchronization. Moreover, the dynamics of neurons become periodic and the frequency of bursts in synchronization manifold increases with decreasing derivative order, contrary to the behavior of a single neuron.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Oana Brandibur, Eva Kaslik
Summary: This work aims to describe the dynamics of a fractional-order coupled FitzHugh-Nagumo neuronal model, analyzing the stability of equilibrium states in terms of their fractional orders and providing numerical simulations to clarify the theoretical results.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Afshin Farhadi, Emmanuel Hanert
Summary: This study investigates the influence of the lambda-truncated fractional-order diffusion operator on the spatial propagation of epidemics caused by infectious diseases. The results show that different asymptotic behaviors of the travelling-wave solutions can be identified depending on the value of lambda.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Hossein Ghasem Damghani, Fahimeh Nazarimehr, Sajad Jafari, Julien C. Sprott
Summary: This paper introduces two new three-dimensional chaotic oscillators, each with a different type of semi-fractal equilibrium curve: one with an R domain semi-fractal curve and one with a circular parametric semi-fractal curve. Both oscillators utilize the Weierstrass function as a basis in their equations. Various properties of these oscillators, including bifurcation, multistability, and fractal basins of attraction, are investigated. The proposed system is considered typical, similar to chaotic systems in previous references, but with the addition of fractal equilibria.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Biology
Sheida Ansarinasab, Fatemeh Parastesh, Farnaz Ghassemi, Karthikeyan Rajagopal, Sajad Jafari, Dibakar Ghosh
Summary: Attention Deficit Hyperactivity Disorder (ADHD) is a common psychological disorder in children, leading to improper recognition of others' emotions. Children with ADHD often struggle with social interaction and lack self-confidence. This study investigates the synchronization patterns in simulated brain networks of boys with ADHD and healthy boys during different facial emotions, using electroencephalogram (EEG) signals. The findings suggest higher synchronization in the frontal and occipital brain lobes of the ADHD group, particularly during happy emotions, indicating deficits in emotional and visual processing centers.
COMPUTERS IN BIOLOGY AND MEDICINE
(2023)
Article
Engineering, Electrical & Electronic
Ramesh Ramamoorthy, Nestor Tsafack, Nasr Saeed, Sifeu Takougang Kingni, Karthikeyan Rajagopal
Summary: This paper investigates the dynamical behavior and system-on-chip realization of current modulation based vertical cavity surface-emitting lasers (CM-VCSEL), and their applications to medical image encryption using compressive sensing (CS). Antimonotonicity phenomenon, chaotic attractor, and chaotic bubble attractor are discovered in CM-VCSEL. The system-on-chip realization verifies the existence of chaotic attractor and chaotic bubble attractor in the experimental setup. A new encryption scheme based on parallel compressive sensing is proposed, using the modulation amplitude of CM-VCSEL and fractional Fourier transform (FrFT) to construct the keys. Performance analysis and comparative experiments demonstrate the effectiveness of the proposed scheme.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
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
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
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
Ahmed M. Ali Ali, Sridevi Sriram, Hayder Natiq, Atefeh Ahmadi, Karthikeyan Rajagopal, Sajad Jafari
Summary: This paper presents a novel one-dimensional trigonometric chaotic map that is multi-stable. The stability conditions and behaviors of the map are analyzed and validated, and the influence of parameter variations on the map's outputs is examined through bifurcation diagrams and Lyapunov exponent spectra.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2023)
Article
Physics, Multidisciplinary
Rending Lu, Prasina Alexander, Hayder Natiq, Anitha Karthikeyan, Sajad Jafari, Jiri Petrzela
Summary: This study investigates the dynamics of the simple Sprott-B chaotic system using fractional-order derivatives. Bifurcation diagrams reveal the presence of coexisting attractors, and the synchronization behavior of the system is examined for various derivative orders. Theoretical findings are validated through the implementation of integer-order and fractional-order electronic circuits. This research contributes to a deeper understanding of the Sprott-B system and its fractional-order dynamics, with potential applications in diverse fields such as chaos-based secure communications and nonlinear control systems.
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
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.
