Article
Optics
T. I. A. N. Q. I. Xu, S. H. A. O. N. A. N. Zheng, Y. A. N. G. Qiu, X. I. N. G. Y. A. N. Zhao, Q. I. Z. E. Zhong, Y. U. A. N. Dong, L. I. A. N. X. I. Jia, T. I. N. G. Hu
Summary: Tunable slow and fast light generation in a silicon-on-insulator Fano resonator is proposed and experimentally demonstrated. The transition from slow light to fast light and from fast light to slow light is achieved by controlling the phase difference of the optical beams coupled into the resonator using a microheater. The results show the potential of this approach for on-chip optical signal processing applications.
Article
Physics, Fluids & Plasmas
Thomas Erneux, Gregory Kozyreff
Summary: Gain switching is a simple technique that generates short pulses through direct modulation of optical gain in lasers. In this study, an asymptotic theory is developed to match slow and fast solutions through an intermediate solution, providing a mathematical analysis of the laser problem. The transition layer is shown to have a significant effect on pulse intensity. Additionally, the theory is applied to sustained laser pulses generated through the Q-switching technique.
Article
Mathematics, Interdisciplinary Applications
Jiahao Zhao, Yibo Xia, Xiaofang Zhang, Qinsheng Bi
Summary: This paper explores the impact of coexisting attractors in the fast subsystem of a nonlinear system on complex dynamics. By analyzing a modified 3D van der Pol-Duffing circuit, the coexistence of five attractors with a hidden one is reported. The study establishes a slow-fast model with two-scale coupling in the frequency domain by introducing a parametric excitation. The coexistence conditions and coexisting attractors including equilibrium points and limit cycles are derived. Different types of bursting oscillations are observed with varying exciting amplitude, and the mechanism behind it is revealed using a modified slow-fast analysis method. The paper also suggests that the presence of coexisting attractors in the fast subsystem can lead to coexisting bursting solutions in the full system, with trajectories visiting different attracting basins or resulting in merged bursting motions.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Mathematics, Applied
Ludovic Righetti, Jonas Buchli, Auke Jan Ijspeert
Summary: This paper investigates the process of transforming oscillators into adaptive frequency oscillators through an adaptation mechanism and demonstrates the fast-slow dynamics involved. The study shows that the input signal forces the dynamics to jump between stable and unstable invariant slow manifolds, resulting in exponential convergence of frequency adaptation.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
(2021)
Article
Mathematics, Applied
Naziru M. Awal, Irving R. Epstein, Tasso J. Kaper, Theodore Vo
Summary: Symmetry-breaking in coupled, identical, fast-slow systems leads to a diverse range of dynamic behaviors, including significant differences in amplitude and frequency as well as qualitatively distinct rhythms between oscillators associated with different functional states. A novel method is presented to analyze these systems, identifying key geometric structures responsible for the symmetry-breaking and demonstrating the robust emergence of various types of symmetry-breaking rhythms. The method is illustrated with two prototypical fast-slow systems: the van der Pol equation describing electrical circuits and the Lengyel-Epstein model of chemical oscillators.
Article
Mathematics, Interdisciplinary Applications
Xiujing Han, Jin Song, Yong Zou, Qinsheng Bi
Summary: This study reports the effects of a small perturbation of excitation frequency on fast-slow oscillations, revealing that a small perturbation of excitation frequency may complicate the vector field of the fast subsystem, leading to complex bifurcation behaviors and finally giving rise to complex fast-slow oscillations.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Honglan Zhu, Xuebing Zhang, Guanglan Wang, Ling Wang
Summary: In this paper, we investigate a delayed diffusive predator-prey model affected by toxic substance. We establish the boundedness and persistence property of the model and analyze the conditions for the existence of Hopf bifurcation, Turing bifurcation and Turing-Hopf bifurcation by analyzing the associated characteristic equation. Further, we study the effects of delay on Hopf bifurcation and Turing-Hopf bifurcation. Numerical simulations confirm the theoretical results and indicate that toxic substance greatly affects the system.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Mathematics
Yining Xie, Jing Zhao, Ruizhi Yang
Summary: This paper proposes a diffusive predator-prey model with a strong Allee effect and nonlocal competition in the prey and a fear effect and gestation delay in the predator. The study mainly focuses on the local stability of the coexisting equilibrium and the existence and properties of Hopf bifurcation. Bifurcation diagrams with the fear effect parameter (s) and the Allee effect parameter (a) are provided, showing that the stable region of the coexisting equilibrium increases (or decreases) with an increase in the fear effect parameter (s) (or the Allee effect parameter (a)). The results demonstrate that the fear effect parameter (s), the Allee effect parameter (a), and gestation delay (t) can be utilized to control the growth of prey and predator populations.
Article
Computer Science, Information Systems
Linhe Zhu, Fan Yang, Gui Guan, Zhengdi Zhang
Summary: This study explores a rumor propagation model on complex networks, introducing a saturation treatment function and considering comprehensive influence factors. Mathematical analyses are conducted to determine the basic reproduction number and stability conditions of rumor propagation, propose targeted immunization control and optimal control strategies, and validate theoretical results through numerical simulations.
INFORMATION SCIENCES
(2021)
Article
Engineering, Mechanical
Yuye Li, Huaguang Gu, Yanbing Jia, Kaihua Ma
Summary: This paper proposes a novel fast-slow variable dissection method with two slow variables to analyze complex bursting behavior, addressing issues encountered with traditional methods and providing insights for modulating pathological pain.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Pankaj Kumar, Dipesh
Summary: This paper applies a mathematical model to investigate the effect of delay in allelochemical density on plant population. The constructed nonlinear delay differential equation system includes three state variables: plant populations (P-1 & P-2) and allelochemical density (T). It is assumed that the presence of allelochemical density affects plant populations, by delaying the conversion of resources and adversely affecting plant population. The study calculates equilibrium points and uses the Routh-Hurwitz theorem to obtain explicit formulations defining stability and the path of Hopf-bifurcation periodic solutions at positive equilibrium. Numerical simulation and graphical support using MATLAB are provided to validate the analytical findings.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics
Liqin Liu, Chunrui Zhang
Summary: This paper studies a system of four coupled van der Pol oscillators with delay. The conditions for the existence of multiple periodic solutions of the system are given. The spatiotemporal patterns of the system are obtained using symmetric Hopf bifurcation theory. Numerical simulations are used to demonstrate the theoretical results.
Article
Physics, Multidisciplinary
Yaru Liu, Shenquan Liu, Bo Lu, Juergen Kurths
Summary: This article explores the dynamics of mixed-mode oscillations (MMOs) in the auditory cortex based on the calcium-based inner hair cells (IHCs) model, revealing the mechanism of MMOs generation using the geometric singular perturbation theory (GSPT). The analysis shows that system parameters control the oscillation patterns in the IHCs model, with many new oscillations occurring. The study also conducts dynamic analysis using slow-fast analysis and bifurcation analysis, uncovering the underlying dynamic properties of perturbed systems under singular perturbation theory.
Article
Automation & Control Systems
Yuzhen Qin, Yu Kawano, Brian D. O. Anderson, Ming Cao
Summary: This article presents new criteria for the partial exponential stability of a slow-fast nonlinear system and applies it to the study of remote synchronization of Kuramoto-Sakaguchi oscillators. Detuning the central mediating oscillator's natural frequency increases synchronization robustness.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Mathematics, Applied
Ahmad Suleman, Rizwan Ahmed, Fehaid Salem Alshammari, Nehad Ali Shah
Summary: This paper examines the complex dynamics of a slow-fast predator-prey interaction with herd behavior. Through bifurcation theory, it is shown that the model experiences both period-doubling and Neimark-Sacker bifurcations at the interior fixed point. Chaos is controlled using the hybrid control approach under the influence of these bifurcations. Numerical simulations highlight the complexity of the model and demonstrate agreement with analytical findings. Using the slow-fast factor as the bifurcation parameter reveals that the model undergoes a Neimark-Sacker bifurcation for larger values of the slow-fast factor at the interior fixed point.
Article
Mathematics, Applied
Mohanasubha Ramasamy, Suresh Kumarasamy, Ashokkumar Srinivasan, Pavithra Subburam, Karthikeyan Rajagopal
Summary: This study investigates the influence of higher-order interactions on network synchronization in fractional-order complex systems. The results show that higher-order interactions contribute to earlier synchronization, and lower fractional-order values accelerate the synchronization process. The findings are validated using multiple models.
Article
Mathematics, Applied
Pragjyotish Bhuyan Gogoi, Suresh Kumarasamy, Awadhesh Prasad, Ram Ramaswamy
Summary: This study investigates a system of coupled nonlinear oscillators with interaction modulated by their similarity. It explores a new route to oscillation death through a Hopf bifurcation, where individual oscillators transition from inhomogeneous limit cycles to different fixed points. The results include analytical and numerical findings for Stuart-Landau oscillators, as well as numerical results for coupled Rossler and Sprott oscillators.
Article
Mathematics, Interdisciplinary Applications
Salem Alkhalaf, Suresh Kumarasamy, Sundaram Arun, Anitha Karthikeyan, Salah Boulaaras
Summary: In this study, the dynamics of one-dimensional fractional-order Rulkov map in biological neurons are presented, showing various dynamical behaviors and the influence of external stimuli on both integer and fractional-order maps. The results are based on the Lyapunov exponent of the fractional-order systems.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Applied
Premraj Durairaj, Sathiyadevi Kanagaraj, Prakash Duraisamy, Anitha Karthikeyan, Karthikeyan Rajagopal
Summary: Vibrational energy harvesters can convert low-frequency broad-band mechanical energy into electrical power, making them suitable for implantable medical devices and wireless sensors. By introducing blinking into the coupling function, we can improve synchronization in bistable energy harvesters with periodic and quasiperiodic excitations. The research shows that increasing the proportion of blinking can initiate synchronization even with lower optimal coupling strength.
Article
Physics, Condensed Matter
Rajamani Samikkannu, Mohanasubha Ramasamy, Suresh Kumarasamy, Karthikeyan Rajagopal
Summary: In this study, we investigate the phenomenon of ghost vibrational resonance in single and one-way coupled plasma oscillator systems with multi-frequency driving forces. We identify that the origin of ghost-vibrational resonance is caused by the high frequency at the missing fundamental frequency ?(0). Our analysis shows undamped signal propagation and enhanced signal amplification in unidirectionally coupled networks of plasma oscillators. Additionally, we report that the response amplitude Q(?(0)) at the missing fundamental frequency is independent of other parameters in the coupled dynamical system and only depends on the coupling constant.
EUROPEAN PHYSICAL JOURNAL B
(2023)
Review
Food Science & Technology
Chukwuebuka Egbuna, Kingsley C. Patrick-Iwuanyanwu, Eugene N. Onyeike, Johra Khan, Santwana Palai, Sandip B. Patel, Vijaykumar K. Parmar, Garima Kushwaha, Omkar Singh, Jaison Jeevanandam, Suresh Kumarasamy, Chukwuemelie Zedech Uche, Mathiyazhagan Narayanan, Mithun Rudrapal, Uchenna Odoh, Ikenna Chikeokwu, Mihnea-Alexandru Gaman, Kaliyaperumal Saravanan, Jonathan C. Ifemeje, Shahira M. Ezzat, Michael C. Olisah, Chukwudi Jude Chikwendu, Kamoru A. Adedokun, Sikiru O. Imodoye, Ibrahim O. Bello, Hannington Twinomuhwezi, Chinaza Godswill Awuchi
Summary: This systematic review identified bioactive compounds with antileukemic properties for the treatment of acute myeloid leukemia (AML). The review found that AML is a heterogeneous malignancy arising from dysregulation of cell differentiation, proliferation, and cell death. Despite advances in treatment strategies, resistance and relapse remain major clinical challenges. The review identified over 60 bioactive compounds in five major groups, each with different mechanisms of action, including disrupting chromatin structure and regulating DNA repair and cell cycle processes.
FOOD SCIENCE & NUTRITION
(2023)
Article
Biology
Sathiyadevi Kanagaraj, Premraj Durairaj, Sivaperumal Sampath, Anitha Karthikeyan, Karthikeyan Rajagopal
Summary: Locally active memristors can mimic neural synapses and generate rich neuro-morphological dynamics in biological neurons. Coupled Hindmarsh-Rose neurons exhibit synchronization behavior under different network connectivities.
Article
Mathematics, Interdisciplinary Applications
Mohanasubha Ramasamy, Suresh Kumarasamy, Sakthi Kumar Sampathkumar, Anitha Karthikeyan, Karthikeyan Rajagopal
Summary: This study conducts an in-depth exploration into the stability of synchronization within discrete nonlinear systems. The findings highlight the existence of stable synchronization manifolds only in distinct coupling schemes, and a comprehensive analysis of the master stability function's behavior across various coupling strengths and system parameters. These results greatly enhance our understanding of network dynamics.
Article
Energy & Fuels
Sabarathinam Srinivasan, Suresh Kumarasamy, Zacharias E. Andreadakis, Pedro G. Lind
Summary: In order to face the challenges of climate change, the European Union has set a target of increasing the share of renewable power to 75% by 2050. Although renewable energy sources have become cleaner and cheaper, their strong fluctuations pose uncertainties in predicting power outcomes and understanding grid phenomena. This review presents various modeling approaches, such as dynamical systems, Bayesian inference, machine learning, and reservoir computing, to help researchers and stakeholders navigate recent advances in power grid research.
Article
Physics, Multidisciplinary
Premraj Durairaj, Sathiyadevi Kanagaraj, P. Nageswara Rao, Anitha Karthikeyan, Karthikeyan Rajagopal
Summary: Magnetic flux and Josephson junctions are crucial in understanding the dynamics of biological neurons, leading to complex behaviors such as chaos and hyper-chaos. These dynamics depend on the coupling strength and junction coefficient.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Physics, Fluids & Plasmas
Premraj Durairaj, Sathiyadevi Kanagaraj, Suresh Kumarasamy, Karthikeyan Rajagopal
Summary: Extreme events are unusual and rare large-amplitude fluctuations that can occur unexpectedly in nonlinear dynamical systems, characterized by events above the extreme event threshold. Different mechanisms and prediction measures for extreme events have been reported. Studies have shown that extreme events are both linear and nonlinear in nature, with rare frequency of occurrence and extreme amplitude. In this Letter, we report on a special class of nonchaotic and nonperiodic extreme events that appear between quasiperiodic and chaotic dynamics of the system. We demonstrate the existence of such extreme events with various statistical measures and characterization techniques.
Article
Optics
S. Leo Kingston, Marek Balacerak, Suresh Kumarasamy, Tomasz Kapitaniak
Summary: In this study, a Zeeman laser model exhibited a rich variety of large-intensity pulses. These instabilities in the system occur through quasiperiodic intermittency, Pomeau-Manneville intermittency, and the breakdown of quasiperiodic motion to chaos followed by an interior crisis. The Zeeman laser model is capable of exploring major types of instabilities when changing system parameters. The statistical analysis revealed the low probability of large-intensity pulses above a threshold value, following an exponential decay that resembles a Poisson-like distribution. The impact of noise and time delay effects near the transition point of the system was also analyzed.
Article
Physics, Fluids & Plasmas
Suresh Kumarasamy, Malay Banerjee, Vaibhav Varshney, Manish Dev Shrimali, Nikolay V. Kuznetsov, Awadhesh Prasad
Summary: Hidden attractors, which are not associated with equilibria, are present in many nonlinear dynamical systems and are difficult to locate. This research letter presents the route to hidden attractors in systems with stable equilibrium points and in systems without any equilibrium points. The study shows that hidden attractors emerge as a result of the saddle-node bifurcation of stable and unstable periodic orbits. Real-time hardware experiments were conducted to demonstrate the existence of hidden attractors in these systems. The findings provide insights into the generation of hidden attractors in nonlinear dynamical systems.
Article
Physics, Fluids & Plasmas
K. Sathiyadevi, D. Premraj, Tanmoy Banerjee, M. Lakshmanan
Summary: This study investigates the impact of additional complex conjugate feedback on globally coupled Stuart-Landau oscillators, revealing phenomena such as symmetry breaking clusters, out-of-phase clusters, explosive amplitude death, and disparate multistable states. By characterizing the first-order transition and hysteresis nature through the amplitude order parameter, mapping global dynamical transitions in parametric spaces, analyzing bifurcation scenarios of the reduced model, and exploring basin stability, the research sheds light on emergent dynamics in the presence of additional feedback.