Article
Engineering, Mechanical
Runan Guo, Junwei Lu, Yongmin Li, Wenshun Lv
Summary: This paper investigates the problem of fixed-time synchronization for delayed complex-valued neural networks with inertial term, proposing two different controllers that can achieve perfect synchronization in a fixed time for networks with different types of activation functions. Synchronization criteria in terms of matrix inequalities and estimates of the settling times are derived, utilizing innovative inequalities in the complex field, representing an advancement of existing research progress. Numerical simulations for various types of activation functions are provided to support the theoretical results.
NONLINEAR DYNAMICS
(2021)
Article
Computer Science, Artificial Intelligence
Shuaibing Zhu, Jin Zhou, Quanxin Zhu, Na Li, Jun-An Lu
Summary: This study addresses the adaptive exponential synchronization problem of complex networks with nondifferentiable time-varying delay. It proposes a delay differential inequality for dealing with the exponential stability of delayed nonlinear systems. The boundedness of the adaptive control gain is theoretically proved. The AES criteria for networks with general delay are established by using the proposed inequality and the boundedness of the control gain.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Mathematics, Applied
N. Jayanthi, R. Santhakumari, Grienggrai Rajchakit, Nattakan Boonsatit, Anuwat Jirawattanapanit
Summary: This study investigates the asymptotic and cluster synchronization issues of coupled delayed complex-valued neural network models with leakage delay in finite time. Several sufficient conditions for asymptotic synchronization and finite-time synchronization are described utilizing the Lyapunov theory and the Filippov regularization framework.
Article
Computer Science, Artificial Intelligence
Dan Yang, Xiaodi Li, Shiji Song
Summary: This article studies the finite-time synchronization problem of delayed complex dynamical networks (CDNs) with impulses, and establishes sufficient conditions for finite-time synchronization. The impact of synchronizing and desynchronizing impulses on the settling time of synchronization is analyzed, and theoretical analysis is verified by simulation examples.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Automation & Control Systems
Xiaolin Yuan, Guojian Ren, Yongguang Yu, Wenjiao Sun
Summary: This paper investigates the mean-square pinning control problem of fractional stochastic discrete-time complex networks. It establishes a new model with stochastic noise and develops pinning controllers and sufficient conditions for the complex networks. By utilizing Lyapunov energy function theory and matrix analysis theory, it proves that synchronization of the networks can be achieved in a mean-square sense via pinning control. Furthermore, these results are extended to solve the synchronization problem of general fractional discrete-time complex networks without noise.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Nattakan Boonsatit, Santhakumari Rajendran, Chee Peng Lim, Anuwat Jirawattanapanit, Praneesh Mohandas
Summary: The issue of adaptive finite-time cluster synchronization for neutral-type coupled complex-valued neural networks with mixed delays is examined in this research. A new adaptive control technique is developed to achieve finite-time synchronization of the networks. The effectiveness of the proposed method is demonstrated through simulation studies.
FRACTAL AND FRACTIONAL
(2022)
Article
Computer Science, Information Systems
Mei Liu, Huitao Zhao, Haijun Jiang, Cheng Hu, Zhiyong Yu, Zhanfeng Li
Summary: This paper focuses on the problem of fixed-time (FXT) and preassigned-time (PAT) synchronization for delayed dynamic complex networks. New results for delayed networks model to ensure the synchronization of FXT and PAT are obtained. Looser conditions for FXT synchronization and more accurate settling time (ST) estimates are established. PAT synchronization with limited control gains is investigated and the synchronization time can be specified in advance based on practical need.
Article
Physics, Multidisciplinary
Mei Liu, Binglong Lu, Zhanfeng Li, Haijun Jiang, Cheng Hu
Summary: This paper investigates the fixed-time synchronization problem for delayed dynamical complex networks and proposes new results and methods to achieve fixed-time synchronization. By designing adaptive controllers and discontinuous feedback controllers, fixed-time synchronization can be achieved by adjusting the main control parameters. The introduction of a new theorem aims to reduce conservatism in existing work, including conditions and synchronization time estimates.
Article
Computer Science, Information Systems
Qiaokun Kang, Qingxi Yang, Zhilong Lin, Qintao Gan
Summary: This paper focuses on the finite-time cluster synchronization issues for a class of delayed fractional-order fully complex-valued community networks, proposing a new mathematical expression and controller design method. The feasibility and effectiveness of the results are demonstrated through simulation examples.
Article
Mathematics
Junmei Guo, Chunrui Ma, Xinheng Wang, Fangfang Zhang, Michael Antonie van Wyk, Lei Kou
Summary: This paper first studied the time chaotic attractor, parameter space and dynamic characteristics of the system, then designed the MFPDFS synchronous controller to achieve synchronization of time-delay fractional complex systems, and finally verified the secure speech transmission through numerical simulation.
Article
Automation & Control Systems
Ling Liu, Wuneng Zhou, Cong Huang
Summary: This article focuses on the finite-time and prescribed-time cluster synchronization problems of switched complex networks with proportional delays. The paper introduces asynchronous switching law and switching parameters to describe the complex dynamical networks. By applying the stability theory of dynamical systems and the average dwell time approach, the paper develops some criteria in the form of linear matrix inequalities to guarantee such networks' finite/prescribed-time cluster synchronization under the pinning control scheme. Finally, a numerical example is presented to demonstrate the effectiveness of the theoretical results.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Physics, Multidisciplinary
Duolan, Linying Xiang, Guanrong Chen
Summary: In this article, the framework of master stability function is extended to stochastic complex networks with time-delayed coupling. The effects of noise, time delay, and their interactions on network synchronization are explored. It is found that increasing the noise intensity can enhance network synchronizability when there is time-delayed coupling and noise diffusion through all state variables of nodes; otherwise, noise can have either positive or negative effects. In stochastic networks, large time delays cause desynchronization. These findings provide valuable insights for designing optimal complex networks in practical applications.
Article
Mathematics, Interdisciplinary Applications
Lu Wang, Xujun Yang, Hongjun Liu, Xiaofeng Chen
Summary: This paper investigates the synchronization in finite time of fractional-order complex-valued gene networks with time delays. Several sufficient conditions for the synchronization in finite time of the relevant network models are explored using feedback controllers and adaptive controllers. The setting time of the response is then estimated using the theory of fractional calculus. Finally, a numerical example is presented to validate the theoretical results, demonstrating that the setting time based on the adaptive controller is shorter than that based on the feedback controller.
FRACTAL AND FRACTIONAL
(2023)
Article
Computer Science, Interdisciplinary Applications
Wanli Zhang, Xinsong Yang, Shiju Yang, Ahmed Alsaedi
Summary: This paper investigates finite-time and fixed-time bipartite synchronization of complex networks with signed graphs, proposing control schemes and establishing synchronization criteria. Numerical simulations validate the new results.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Engineering, Multidisciplinary
Juan Chen, Xinru Li, Xiaoqun Wu, Ganbin Shen
Summary: This paper focuses on the prescribed-time synchronization of complex dynamical networks (CDNs) with and without time-varying delays. Suitable controllers are designed to obtain CDNs with directed spanning trees. Two sufficient conditions are derived using Lyapunov Stability Theory to ensure that CDNs reach synchronization within a prescribed finite time. Unlike existing works, where the settling time is determined by initial conditions or control parameters, the proposed method allows for arbitrary assignment of the settling time as needed. Two examples are provided to validate the theoretical results.
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2022)
Article
Automation & Control Systems
Lingzhi Zhao, Yongzheng Sun, Haifeng Dai, Donghua Zhao
Summary: This paper investigates the fixed-time stochastic consensus problem of multi-agent systems with fixed and switching topologies. A class of continuous non-Lipschitz protocols are designed to achieve fixed-time stochastic consensus, with effective rigorously proven. Sufficient conditions for consensus are established based on stability theory of stochastic differential equations, and the influence of algebraic connectivity on convergence time is investigated. Simulations illustrate that convergence time depends on control term parameters and suitable noise can expedite consensus.
INTERNATIONAL JOURNAL OF CONTROL
(2021)
Article
Physics, Multidisciplinary
Wang Li, Xinjie Fu, Yongzheng Sun, Maoxing Liu
Summary: In this study, an SEAIRS model for the COVID-19 epidemic on networks was established and analyzed. The basic reproduction number R-0 was derived using the next-generation matrix method, showing the significant role of asymptomatic infectors in disease spreading. It was analytically demonstrated that the disease-free equilibrium is stable if R-0 is less than or equal to 1. Additionally, the effects of various quarantine strategies were investigated and compared through numerical simulations.
FRONTIERS IN PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Wang Li, Lingzhi Zhao, Hongjun Shi, Donghua Zhao, Yongzheng Sun
Summary: This paper investigates the generalized outer synchronization between two coupled dynamical networks, proposing a new stochastically adaptive coupling method. The adaptive stochastic coupling can achieve generalized outer synchronization and optimize time and energy costs by adjusting gain rapidly and randomly. This study extends the applications of adaptive control technology and enhances understanding of the constructive role of noise on network synchronization.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Automation & Control Systems
Xiaofei Zhang, Haifeng Dai, Lingzhi Zhao, Donghua Zhao, Yongzheng Sun
Summary: This paper investigates the flocking problems of Cucker-Smale systems, proposing sufficient conditions and studying the impact of control parameters on convergence speed. Finally, numerical simulations are used to validate the theoretical results.
INTERNATIONAL JOURNAL OF CONTROL
(2022)
Article
Engineering, Multidisciplinary
Haifeng Dai, Wang Li, Chunyu Yang, Guanghui Wen, Yongzheng Sun
Summary: This paper proposes a new switching protocol using linear feedback and finite-time control technologies to solve the finite-time consensus problem of multi-agent networks. Analytical estimates reveal the network characteristics and control parameters that can reduce time and energy costs, showing a trade-off between the two where reducing time cost will increase energy cost.
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2021)
Article
Mathematics, Applied
Nan Liang, Maoxing Liu, Yongzheng Sun, Rui Xiao, Lingzhi Zhao
Summary: This paper investigates the time and energy costs for achieving synchronization of the Kuramoto-oscillator network with or without noise perturbation. A novel switching controller is designed to achieve synchronization and optimize time and energy consumption, combining the advantages of both the proportional feedback control method and the finite-time control technology. Sufficient conditions for achieving synchronization are established, and the estimates of time and energy costs are obtained mathematically. The study reveals a trade-off between time and energy costs, where adjusting the control parameters can reduce energy consumption but will inevitably increase time cost.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2022)
Article
Automation & Control Systems
Wang Li, Yue Qiao, Jiaming Wu, Hongjun Shi, Yongzheng Sun
Summary: In this paper, the adaptive pinning synchronization problem of complex networks with partial delay and noise coupling is investigated. Realistic complex networks with partial delay and noise perturbation are first established. By combining the advantages of the adaptive control method and pinning control technology, a novel coupling is designed to achieve synchronization. Several sufficient criteria for almost sure outer synchronization are developed based on the LaSalle invariance principle for stochastic differential equations. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed synchronization scheme.
INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS
(2023)
Article
Computer Science, Interdisciplinary Applications
Wang Li, Haifeng Dai, Lingzhi Zhao, Donghua Zhao, Yongzheng Sun
Summary: In this paper, the influence of noise on the consensus of leader-following multi-agent systems is explored. Conditions for achieving consensus in the presence of noise are obtained using algebraic graph theory and stability theory of stochastic differential equations. The results reveal the positive role of noise in the emergence of consensus. Numerical simulations are provided to demonstrate the analytical results.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Automation & Control Systems
Jiaqi Chang, Hongjun Shi, Song Zhu, Donghua Zhao, Yongzheng Sun
Summary: This article investigates the estimation of time cost for stochastic consensus of second-order nonlinear multiagent systems (MASs), taking into account the effects of noise and nonlinear inherent dynamics of agents. Pinning protocols are designed to achieve finite/fixed-time stochastic consensus while minimizing energy consumption, by controlling only a small fraction of agents. Sufficient conditions for stochastic consensus are established using stability theory of stochastic differential equations and algebra graph theory. The proposed protocols are validated through numerical simulation on the consensus of unmanned aerial vehicles (UAVs) system.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Mathematics, Applied
Rui Xiao, Wang Li, Donghua Zhao, Yongzheng Sun
Summary: Coordinated directional switches can emerge in moving biological groups through social and delayed interactions. The study investigates the influence of social interactions on ordered directional switching behavior in swarming systems with various network structures. Results show that the interplay between social and delayed interactions plays a crucial role in regulating directional switching behavior. The study highlights the effects of social and delayed interactions on ordered directional switching motion.
Article
Automation & Control Systems
Xiangxin Yin, Rui Xiao, Haifeng Dai, Quanxin Zhu, Yongzheng Sun
Summary: In this article, the synchronization of multiplex networks with random topologies and any number of layers is studied. A general framework is proposed for analyzing the synchronization of multiplex networks with or without layer similarity. Using random matrix theory, sufficient conditions of synchronization for multiplex networks under strong and weak interlayer coupling are obtained. It is shown, both analytically and numerically, that increasing layer similarity can first promote and then hinder synchronization for weak interlayer coupling, while synchronization can be suppressed for strong interlayer coupling. However, increasing the number of layers can always facilitate synchronization only if the interlayer coupling is strong. Finally, the theoretical results are verified by numerical simulations.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Computer Science, Interdisciplinary Applications
Ruyi Sun, Jiaqi Chang, Hongmei Wang, Miaomiao Li, Yongzheng Sun
Summary: This paper studies the finite-time and fixed-time synchronization problems of multi-layer networks. Two novel switching controllers are proposed and their effectiveness is verified using Lyapunov stability theory. It is found that there is a trade-off between time and energy costs, and adjusting parameters can minimize the total cost.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
Article
Mathematics
Jiaqi Chang, Xiangxin Yin, Caoyuan Ma, Donghua Zhao, Yongzheng Sun
Summary: This paper investigates the finite-time and fixed-time stochastic synchronization of complex networks with pinning control. By considering the time and energy cost of control, efficient protocols are proposed by combining the advantages of finite-time control technology and pinning control technology. The influence of noise is taken into account and sufficient conditions for the network to achieve stochastic synchronization in a finite time are given in this study. Based on the stability theory of stochastic differential equations, the upper bound of the setting time is estimated. Finally, the effects of control parameters, noise intensity, and the number of control agents on the network synchronization rate are studied. Numerical simulations validate the theoretical results.
ELECTRONIC RESEARCH ARCHIVE
(2022)
Article
Physics, Multidisciplinary
Yongzheng Sun, Wang Li, Liang Li, Guanghui Wen, Sandro Azaele, Wei Lin
Summary: This study investigates the influence of time-delay interactions on the collective motion of swarming locusts. The results show that different types of time delays can affect directional switches, with small response delays increasing the mean switching time and large response delays potentially destroying ordered switches.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Multidisciplinary Sciences
Duxin Chen, Yongzheng Sun, Guanbo Shao, Wenwu Yu, Hai-Tao Zhang, Wei Lin
Summary: Investigated the mechanism governing the coordinated rotational flight of pigeon flocks, using sparse Bayesian learning method, revealed the decision-making process of rotational switching flight is more nonlinear, established a data-driven particle model with two potential wells and estimated the mean switching time for rotational direction.
ROYAL SOCIETY OPEN SCIENCE
(2021)
Article
Mathematics, Applied
Hao Liu, Yuzhe Li
Summary: This paper investigates the finite-time stealthy covert attack on reference tracking systems with unknown-but-bounded noises. It proposes a novel finite-time covert attack method that can steer the system state into a target set within a finite time interval while being undetectable.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Nikolay A. Kudryashov, Aleksandr A. Kutukov, Sofia F. Lavrova
Summary: The Chavy-Waddy-Kolokolnikov model with dispersion is analyzed, and new properties of the model are studied. It is shown that dispersion can be used as a control mechanism for bacterial colonies.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Qiang Ma, Jianxin Lv, Lin Bi
Summary: This paper introduces a linear stability equation based on the Boltzmann equation and establishes the relationship between small perturbations and macroscopic variables. The numerical solutions of the linear stability equations based on the Boltzmann equation and the Navier-Stokes equations are the same under the continuum assumption, providing a theoretical foundation for stability research.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Samuel W. Akingbade, Marian Gidea, Matteo Manzi, Vahid Nateghi
Summary: This paper presents a heuristic argument for the capacity of Topological Data Analysis (TDA) to detect critical transitions in financial time series. The argument is based on the Log-Periodic Power Law Singularity (LPPLS) model, which characterizes financial bubbles as super-exponential growth (or decay) with increasing oscillations approaching a tipping point. The study shows that whenever the LPPLS model fits the data, TDA generates early warning signals. As an application, the approach is illustrated using positive and negative bubbles in the Bitcoin historical price.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Xavier Antoine, Jeremie Gaidamour, Emmanuel Lorin
Summary: This paper is interested in computing the ground state of nonlinear Schrodinger/Gross-Pitaevskii equations using gradient flow type methods. The authors derived and analyzed Fractional Normalized Gradient Flow methods, which involve fractional derivatives and generalize the well-known Normalized Gradient Flow method proposed by Bao and Du in 2004. Several experiments are proposed to illustrate the convergence properties of the developed algorithms.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Lianwen Wang, Xingyu Wang, Zhijun Liu, Yating Wang
Summary: This contribution presents a delayed diffusive SEIVS epidemic model that can predict and quantify the transmission dynamics of slowly progressive diseases. The model is applied to fit pulmonary tuberculosis case data in China and provides predictions of its spread trend and effectiveness of interventions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shuangxi Huang, Feng-Fei Jin
Summary: This paper investigates the error feedback regulator problem for a 1-D wave equation with velocity recirculation. By introducing an invertible transformation and an adaptive error-based observer, an observer-based error feedback controller is constructed to regulate the tracking error to zero asymptotically and ensure bounded internal signals.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Weimin Liu, Shiqi Gao, Feng Xu, Yandong Zhao, Yuanqing Xia, Jinkun Liu
Summary: This paper studies the modeling and consensus control of flexible wings with bending and torsion deformation, considering the vibration suppression as well. Unlike most existing multi-agent control theories, the agent system in this study is a distributed parameter system. By considering the mutual coupling between the wing's deformation and rotation angle, the dynamics model of each agent is expressed using sets of partial differential equations (PDEs) and ordinary differential equations (ODEs). Boundary control algorithms are designed to achieve control objectives, and it is proven that the closed-loop system is asymptotically stable. Numerical simulation is conducted to demonstrate the effectiveness of the proposed control scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Gourav Mandal, Lakshmi Narayan Guin, Santabrata Chakravarty
Summary: The ecological framework investigates the dynamical complexity of a system influenced by prey refuge and alternative food sources for predators. This study provides a thorough investigation of the stability-instability phenomena, system parameters sensitivity, and the occurrence of bifurcations. The bubbling phenomenon, which indicates a change in the amplitudes of successive cycles, is observed in the current two-dimensional continuous system. The controlling system parameter for the bubbling phenomena is found to be the most sensitive. The prediction and identification of bifurcations in the dynamical system are crucial for theoretical and field researchers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Damian Trofimowicz, Tomasz P. Stefanski, Jacek Gulgowski, Tomasz Talaska
Summary: This paper presents the application of control engineering methods in modeling and simulating signal propagation in time-fractional electrodynamics. By simulating signal propagation in electromagnetic media using Maxwell's equations with fractional-order constitutive relations in the time domain, the equations in time-fractional electrodynamics can be considered as a continuous-time system of state-space equations in control engineering. Analytical solutions are derived for electromagnetic-wave propagation in the time-fractional media based on state-transition matrices, and discrete time zero-order-hold equivalent models are developed and their analytical solutions are derived. The proposed models yield the same results as other reference methods, but are more flexible in terms of the number of simulation scenarios that can be tackled due to the application of the finite-difference scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yuhao Zhao, Fanhao Guo, Deshui Xu
Summary: This study develops a vibration analysis model of a nonlinear coupling-layered soft-core beam system and finds that nonlinear coupling layers are responsible for the nonlinear phenomena in the system. By using reasonable parameters for the nonlinear coupling layers, vibrations in the resonance regions can be reduced and effective control of the vibration energy of the soft-core beam system can be achieved.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
S. Kumar, H. Roy, A. Mitra, K. Ganguly
Summary: This study investigates the nonlinear dynamic behavior of bidirectional functionally graded plates (BFG) and unidirectional functionally graded plates (UFG). Two different methods, namely the whole domain method and the finite element method, are used to formulate the dynamic problem. The results show that all three plates exhibit hardening type nonlinearity, with the effect of material gradation parameters being more pronounced in simply supported plates.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Isaac A. Garcia, Susanna Maza
Summary: This paper analyzes the role of non-autonomous inverse Jacobi multipliers in the problem of nonexistence, existence, localization, and hyperbolic nature of periodic orbits of planar vector fields. It extends and generalizes previous results that focused only on the autonomous or periodic case, providing novel applications of inverse Jacobi multipliers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yongjian Liu, Yasi Lu, Calogero Vetro
Summary: This paper introduces a new double phase elliptic inclusion problem (DPEI) involving a nonlinear and nonhomogeneous partial differential operator. It establishes the existence and extremality results to the elliptic inclusion problem and provides definitions for weak solutions, subsolutions, and supersolutions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shangshuai Li, Da-jun Zhang
Summary: In this paper, the Cauchy matrix structure of the spin-1 Gross-Pitaevskii equations is investigated. A 2 x 2 matrix nonlinear Schrodinger equation is derived using the Cauchy matrix approach, serving as an unreduced model for the spin-1 BEC system with explicit solutions. Suitable constraints are provided to obtain reductions for the classical and nonlocal spin-1 GP equations and their solutions, including one-soliton solution, two-soliton solution, and double-pole solution.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
