JournalTOCs

Nonlinear Dynamics
Journal Prestige (SJR): 1.468

Citation Impact (citeScore): 4
Number of Followers: 23

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1573-269X - ISSN (Online) 0924-090X
Published by Springer-Verlag

[2468 journals]

Rogue waves on the periodic wave background in the
Kadomtsev–Petviashvili I equation
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  Abstract: Abstract Rogue waves arising on the background of two families of periodic standing waves in the Kadomtsev–Petviashvili I (KPI) equation are investigated. By the nonlinearization of spectral problem and Darboux transformation approach, the rogue wave solutions of the KPI equation on the Jacobian elliptic functions dn and cn background are derived. Darboux transformation is also used to introduce trigonometric function periodic background for the higher-order rogue wave in the KPI equation. On the plane wave background, some rogue waves, breathers and hybrid waves in the KPI equation are obtained as a byproduct in this paper. Moreover, the results represented in this paper enrich the dynamics of \((2+1)\) dimensional nonlinear wave equations.
  PubDate: 2023-10-01
Analytical study of three-soliton interactions with different phases in
nonlinear optics
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  Abstract: Abstract Excessive nonlinear drift in optical communication systems can lead to splitting of solitons and coexistence of multiple solitons, thereby affecting communication quality. In this paper, we investigate the nonlinear dynamic characteristics of three-soliton interactions in optical fibers. Firstly, we obtained exact three-soliton solution of the nonlinear Schrödinger equation. Then, we conduct theoretical simulations of the formation process of those obtained three solitons. The effects of initial phase, initial spacing and initial amplitude on the interaction of three solitons are discussed, and the evolution of three solitons in optical fibers is analyzed. The transmission characteristics of the interaction of three solitons are studied using theoretical analysis. The relevant conclusions will enrich people’s understanding of the interaction characteristics of multiple solitons and provide theoretical reference for experimental research.
  PubDate: 2023-10-01
The application of the cell mapping method in the characteristic diagnosis
of nonlinear dynamical systems
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  Abstract: Abstract The cell mapping method is one of the most powerful tools in the global analysis of nonlinear dynamical systems. It accurately depicts the boundaries of the domains of attractors but is not the ideal method for diagnosing the characteristics of attractors. To improve the performance of the conventional cell mapping method, an approach telling quasiperiodicity from chaos is developed in the current research. The proposed method uses the convergence speed of a probability distribution on the attractor as the criterion. For a chaotic system, the distribution converges quickly to the invariant density in several iterations. As for a quasiperiodic system, the distribution converges extremely slowly to the invariant density. The difference can be explained by the eigenvalues of the transition matrices of different systems. The transition matrix of a chaotic system has irregular eigenvalues, and the second-largest eigenvalue is small enough, while the matrix of a quasiperiodic system has regular eigenvalues, many of which are close to the unit circle. A theoretical analysis of some simple mappings is addressed to support this explanation. Furthermore, as a supplement to the analysis, a numerical method that calculates the Lyapunov exponent from the transition matrix is also discussed.
  PubDate: 2023-10-01
Analysis of a class of Lorenz-like stochastic resonance model and its
application in induction motor fault diagnosis
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  Abstract: Abstract Stochastic resonance (SR) is a method to enhance weak characteristic signals, but the classical model like Duffing oscillation is limited by fewer parameters when it is applied to detect different signals. Consider chaotic system with the characteristics of adjustable parameters and wide dimensions, from the perspective of chaos to induce SR, which is studied to discover the conversion conditions between chaos and SR system. Firstly, the mechanism of a class of Lorenz-like SR system for SR generation is studied, whose parameters relationship meeting the moving point transition and parameters range satisfying the maximum Lyapunov exponent (MLE) are analyzed. Secondly, within the determined parameters range, the optimal parameters are searched by particle swarm optimization (PSO) to output signal with optimal signal-to-noise ratio (SNR). Finally, the output fault signal after highlighting the characteristics is diagnosed by utilizing extreme learning machine (ELM). The experimental results show that the fault signal is detected and diagnosed efficiently and accurately.
  PubDate: 2023-10-01
Reconstructing a fractal supply chain network based on geographical
characteristics
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  Abstract: Abstract To improve the resilience of the supply chain, this paper selects an “alternative” for supplier nodes in different scale regions based on the self-similarity of geographical structure in the evolution of the supply chain network, so as to realize the reconfiguration of the supply chain. Second, a model for supply chain risk propagation is created. The model assumes that when a supplier node fails as a result of an external shock, an alternative node can take over the seed provider node’s supply function, enhancing the supply chain network’s fault tolerance and recovery. Finally, the real supply chain data of a manufacturing enterprise are obtained, and its structure is reconstructed using the model built in this paper. On this basis, the robustness of the initial supply chain and the fractal supply chain is measured separately, as well as the risk propagation in the two supply chains. The experimental results show that the supply chain structure established in this paper has strong robustness and can better resist risk propagation. This paper breaks through the problem that the construction of a fractal supply chain remains at the theoretical level and forms a concrete and operational industrial application, which has important theoretical and practical values.
  PubDate: 2023-10-01
Nonlinear dynamic analysis of helical gear-rotor-bearing coupled system
based on bearing load calculation with TRB clearance
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  Abstract: Abstract Based on Hertz contact deformation theory, the load distribution of roller and bearing load can be obtained with the consideration of rotating speed and TRB clearance. Furthermore, The TRB load model were introduced into the established dynamic model of helical gear system which includes time varying meshing stiffness(TVMS) of helical gear pair, comprehensive transmission error, gear backlash and bearing mounting style. Dynamic differential equations were solved by Runge–Kutta method. The effect of rotating speed, TRB clearance on the bearing load and dynamic behavior of system were investigated. Results show that input rotating speed and TRB clearance have significant influence on the gear system dynamic behavior. The increase of rotating speed could bring the system into nT-periodic motion, chaotic motion, nT-periodic motion, quasi-periodic motion and chaotic motion. And with the increase of TRB clearance, the system undergoes nT-periodic motion, quasi-periodic motion, and chaotic motion. When the rotating speed is 1000 r/min ~ 2700 r/min, 3200 r/min ~ 4900 r/min or the TRB clearance is less than 5 mm, the system is in nT-periodic motion. When the rotating speed is 4900 r/min ~ 6000 r/min or the TRB clearance is between 5 and 10 mm, the system displays quasi-periodic motion form. When the rotating speed is 2700 r/min ~ 3200 r/min or bigger than 6000 r/min or the bearing clearance exceeds 10 mm, the system is in chaotic motion.
  PubDate: 2023-10-01
Nonlinear dynamics of two dimensional rotor-active magnetic bearing system
with generalized-pole legs: stability state diagram and control strategy
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  Abstract: Abstract The static stability and dynamical behavior of active magnetic bearings made of n arbitrary pairs of electromagnet coils (PEC) are investigated. Nonlinear equations governing the dynamics of the rotor-shaft with two degrees of freedom are derived as a function of n and from which the stability state diagram of the generalized model is established. This diagram is presented as an essential tool in the designing of AMBs and also helps to specify conditions of use for optimal operation of the device. The results highlight its strong dependence, quantitatively and qualitatively, on the number of PEC of the bearing. In the dynamic regime, the obtained frequency-amplitude response of the system shows that the increasing of the number of PEC in the bearing and the choice of the proportional gain of the controller greater than a threshold value lead to the decreasing of the amplitude of vibration of the system and also allows to avoid the appearance of the jump phenomena. Diagrams summarizing procedure leading to the best choice of the characteristic parameters of the bearing and controller have been drawn up.
  PubDate: 2023-10-01
Dynamics of nonlinear dark waves and multi-dark wave interactions for a
new extended (3+1)-dimensional Kadomtsev–Petviashvili equation
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  Abstract: Abstract The Kadomtsev–Petviashvili (KP) equation is widely used to model nonlinear wave phenomena occurring in plasmas and fluids, such as water waves with weak nonlinear restoring forces, and shock waves propagation phenomena in plasma. In this paper, we investigate a new extended ( \(3+1\) )-dimensional KP equation. Based on the Hirota bilinear method, the N-soliton solutions for the equation are derived. By introducing a new constraint to the N-soliton solutions, namely considering different dispersion coefficients to zero, the fission and fusion phenomena in multi solitons have been discovered. Subsequently, the M-lump wave and rogue wave solutions were derived using the long wave limit, and systematically analyzed the dynamics of the lump waves through numerical simulations. Additionally, based on the method mentioned earlier, combined with the complex conjugate construction method, we investigated some novel interaction phenomena such as lump waves with fusion (fission) waves, fusion (fission) waves with breather waves, line rogue waves with lump waves, and so on. These results may provide some explanation for the fission or fusion phenomena occurring in nonlinear models, as well as the complex nonlinear superposition between waves in fluid systems.
  PubDate: 2023-10-01
Soliton resonances, soliton molecules, soliton oscillations and
heterotypic solitons for the nonlinear Maccari system
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  Abstract: Abstract Soliton resonances and soliton molecules have become a hot topic in the field of nonlinear science and engineering in recent years due to their potential applications. This work presents a systematic study of the soliton interaction dynamics of the Maccari system. Using the bilinear method, explicit first- and second-order solutions of the system are derived for the system. With these solutions and carefully chosen parameters, we observe various soliton interaction phenomena, such as soliton resonances, soliton molecules, soliton oscillations, and heterotypic solitons, including the V- and Y-type soliton, for the two dependent variables under two coordinate systems: space and spatiotemporal coordinate systems, respectively. Notably, we find that soliton molecules and heterotypic solitons exhibit completely different features under the two coordinate systems. The constraint conditions for the existence of soliton molecules are more restrictive in the spatiotemporal coordinate, and the occurrence of V- and Y-type soliton patterns is relatively rare in this coordinate system.
  PubDate: 2023-10-01
Lie symmetry analysis, exact solutions, and conservation laws to
multi-component nonlinear Schrödinger equations
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  Abstract: Abstract The multi-component nonlinear Schrödinger equations (MNLS) are derived by extending the single-component nonlinear Schrödinger equation to multiple interacting fields. These equations often describe the dynamics of wave packets in quantum mechanics or nonlinear optics. In this paper, we investigate MNLS equations via the Lie symmetry method. The Lie infinitesimal symmetries of the MNLS equations are derived by solving recursive determining equations, and the symmetry reductions of the equations are given by using symmetry variables. Moreover, some interesting explicit solutions for the equations are constructed. Finally, the conservation laws of the MNLS equations are obtained utilizing Ibragimov’s method with detailed derivation.
  PubDate: 2023-10-01
Dynamics and bifurcation analysis of a delay non-smooth Filippov
Leslie–Gower prey–predator model
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  Abstract: Abstract In this paper, we proposed a Filippov prey–predator model with time delay considering threshold policy control of integrated pest management. The study aims to address how the threshold and time delay influence the dynamics of the model. To do this, the existence and the stability of the equilibria of the subsystems have been explored, and then, we apply Filippov convex method to investigate the sliding domain and sliding mode dynamics. Furthermore, the complex dynamics including stability of equilibrium, sliding dynamics and various bifurcation phenomena with respect to time delay and economic threshold have been investigated in more detail. The system will display types of local (boundary node/focus bifurcation) and global bifurcations (touching, sliding switching and crossing bifurcations) if the time delay crosses some critical values, such that the pest management is challenged for the number of pests will exceed the given tolerant value. These results show how crucial in the pest control to consider time delay.
  PubDate: 2023-10-01
An adaptive event-triggered secondary regulation strategy for microgrids
with communication link faults
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  Abstract: Abstract This paper investigates the event-triggered secondary regulation problem for islanded alternating-current (AC) microgrids with unknown communication link faults. In order to handle unknown time-varying communication link faults and avoid utilizing global information, a distributed secondary regulation strategy is proposed, which achieves voltage and frequency regulations, as well as power sharing. Meanwhile, to save system resources and relieve the communication burden, an adaptive event-triggered mechanism is designed. Finally, an islanded AC microgrid test system is built in MATLAB/SimPowerSystems to validate the proposed strategy. It indicates that the proposed strategy highly reduces the controller updates and increases the reliability of system.
  PubDate: 2023-10-01
Prediction of soliton evolution and equation parameters for NLS–MB
equation based on the phPINN algorithm
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  Abstract: Abstract To enhance the precision and efficiency of result prediction, we proposed a parallel hard-constraint physics-informed neural networks (phPINN) by combining the parallel fully-connected neural network structure and the residual-based adaptive refinement method. We discussed the forward and inverse problems of the nonlinear Schrödinger–Maxwell–Bloch equation via the phPINN. In the forward problem, we predict five forms of soliton solutions and rogue wave dynamics under corresponding initial and boundary conditions; In the inverse problem, we predict the equation parameter using the training data with different noise intensities, initial values, and solution forms. The predicted parameters achieve a relative error of less than 1%. These results validate the effectiveness of the phPINN algorithm in solving forward and inverse problems of three-component coupled equations.
  PubDate: 2023-10-01
The mixed solutions of the (2+1)-dimensional Hirota–Satsuma–Ito
equation and the analysis of nonlinear transformed waves
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  Abstract: Abstract In this paper, we obtain the N-soliton solution for the \((2+1)\) -dimensional Hirota–Satsuma–Ito equation by the Hirota bilinear method. On this basis, the breathers and lumps can be obtained using the complex conjugate parameter as well as the long wave limit method, and the mixed solutions containing them are investigated. Then, different nonlinear transformed waves are obtained from breathers and lumps under specific conditions, which include quasi-anti-dark soliton, M-shaped soliton, oscillation M-shaped soliton, multi-peak soliton, quasi-periodic soliton and W-shaped soliton. Finally, on the basis of the two-breather solutions, we discuss in detail the mixed solutions consisting of one breather and one nonlinear transformed wave, and the mixed solutions formed by two nonlinear transformed waves.
  PubDate: 2023-10-01
Control of impulsive systems via high-order fully actuated system approach
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  Abstract: Abstract This article studies the problem of designing the controller for the stabilization of nonlinear control systems with impulsive effects via high-order fully actuated (HOFA) system approach. A matrix norm inequality that connects the matrix norm to the eigenvalues of the matrix is obtained, providing the theoretical basis for the utilization of the HOFA system approach in controlling high-order nonlinear impulsive systems. The analysis on the closed-loop systems derives the stability criteria of nonlinear control systems with impulsive effects via the HOFA system approach. This work not only extends the application of the HOFA system approach to nonlinear impulsive systems for the first time but also introduces a new nonlinear control technique for the control of impulsive systems. With the proposed approach to design the controller, two examples demonstrate the design procedure and show the effectiveness of the theoretical results.
  PubDate: 2023-10-01
An efficient spam detector model for accurate categorization of spam
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  Abstract: Abstract Even though the widespread distribution of social network platforms offered credible benefits for people to share information, its rapid development has attracted various attackers. In recent times, the threatening activities of spammers increased rigorously resulting in information security vulnerabilities. An efficient spam detector module is required to accurately categorize spam tweets from legitimate tweets. To fulfill this requirement, an effective spam detection mechanism using a multilayer bidirectional stacked recurrent unit-based quantum chaotic butterfly (MBiSR-QCB) approach is designed in this paper. In order to avoid misclassification issues of the proposed MBiSR-QCB approach, expert knowledge is taken into consideration to make optimal decisions. Aiming at reducing the expert’s workload, the tweets are initially processed through the proposed MBiSR-QCB approach, which filters out the non-spam tweets from the spam tweets in a very short duration. The spam tweets distinguished by the proposed MBiSR-QCB approach are further investigated by the expert to prevent the probability of selecting non-spam tweets as spam tweets. The expert performs in-depth analysis and finally categorizes them into true spam tweets and true non-spam tweets. Despite the collaborated operation, the spam detection accuracy achieved is mainly because of the proposed MBiSR-QCB approach. The parallel pattern learning operations of stacked bidirectional gated recurrent unit (SBi-GRU) and multilayer bidirectional long short-term memory (MBiLSTM) with an optimal setting of hyperparameters by quantum chaotic butterfly optimization (QCBO) algorithm increases the spam detection accuracy. The proposed MBiSR-QCB approach’s effectiveness is examined using various metrics such as precision, accuracy, sensitivity, F1-measure, and specificity. The simulation result manifests the enhanced performance of the proposed MBiSR-QCB approach over other compared existing techniques, particularly with higher spam detection accuracy of about 98.7%.
  PubDate: 2023-10-01
Barrier function-based adaptive antisway control for underactuated
overhead cranes
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  Abstract: Abstract Nonlinear controls that account for constraints on the state variable of overhead cranes can hardly strengthen the effective coupling between trolley movement and load oscillation, thus possessing little capacity in oscillation suppression. Nevertheless, such control designs trend to be more complex under parametric uncertainties. To solve these problems, this paper employs novel barrier functions in the coupling control design, so that the obtained feedback can preserve all states, including the composite variable, bounded within asymmetric limits while simultaneously enhancing antisway effectiveness. Owing to the simple structure of the Lyapunov derivative, the adaptation facilitates the proposed controller with robustness to parametric uncertainties. LaSalle’s invariance principle ensures the asymptotic stability, and experiments verify the validity of the suggested controller.
  PubDate: 2023-10-01
Identification of nonlinear conservation laws for multiphase flow based on
Bayesian inversion
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  Abstract: Abstract Conservation laws of the generic form \(c_t+f(c)_x=0\) play a central role in the mathematical description of various engineering related processes. Identification of an unknown flux function f(c) from observation data in space and time is challenging due to the fact that the solution c(x, t) develops discontinuities in finite time. We explore a Bayesian type of method based on representing the unknown flux f(c) as a Gaussian random process (parameter vector) combined with an iterative ensemble Kalman filter (EnKF) approach to learn the unknown, nonlinear flux function. As a testing ground, we consider displacement of two fluids in a vertical domain where the nonlinear dynamics is a result of a competition between gravity and viscous forces. This process is described by a multidimensional Navier–Stokes model. Subject to appropriate scaling and simplification constraints, a 1D nonlinear scalar conservation law \(c_t+f(c)_x=0\) can be derived with an explicit expression for f(c) for the volume fraction c(x, t). We consider small (noisy) observation data sets in terms of time series extracted at a few fixed positions in space. The proposed identification method is explored for a range of different displacement conditions ranging from pure concave to highly non-convex f(c). No a priori information about the sought flux function is given except a sound choice of smoothness for the a priori flux ensemble. It is demonstrated that the method possesses a strong ability to identify the unknown flux function. The role played by the choice of initial data \(c_0(x)\) as well various types of observation data is highlighted.
  PubDate: 2023-10-01
Disturbance observer-based event-triggered fault tolerant control for
coupled spacecraft on SE(3) with actuator saturation and misalignment
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  Abstract: Abstract The fault-tolerant control problem associated with limited communication is addressed in this paper for coupled spacecraft in the presence of internal uncertainties, external disturbances, actuator uncertainties including failures, magnitude deviation and misalignment, and actuator saturation constraint. Firstly, considering the configuration and installation deviation of the thrusters, a six degree of freedom (6-DOF) kinematics and dynamics coupling model of the spacecraft is established and derived on the Lie group SE (3). Then, the lumped disturbance is estimated by using a fixed-time convergent sliding mode surface combined with a disturbance observer. Next, the dynamic event-triggered fault-tolerant controller is proposed for the first time to compensate for the lumped disturbance. Finally, both theoretical analysis and numerical simulation results verify that the method proposed in this paper can not only achieve fast and high-precision tracking control goal, moreover, through comparative analysis, but the data transmission frequency between the controller and the actuator are also effectively reduced, thereby significantly reducing the communication burden of the spacecraft.
  PubDate: 2023-10-01
Riemann–Hilbert method and soliton dynamics for a mixed spectral complex
mKdV equation with time-varying coefficients
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  Abstract: This paper reports the feasibility of using Riemann–Hilbert method (RHM) to reveal the soliton dynamics with variable velocity and amplitude in mixed spectral nonlinear integrable systems. To achieve this goal, we consider a novel mixed spectral complex mKdV equation (mscmKdV) with time-varying coefficients. Firstly, Lax representation of the time-varying coefficient mscmKdV equation is first abstracted from Ablowitz–Kaup–Newell–Segur (AKNS) matrix spectral problem equipped with a mixed spectrum. With the help of the Lax representatoin, a Riemann–Hilbert problem (RHP) associating with the mscmKdV equation is then established. Due to the confirmation of solvability of the RHP, scattering data used for reconstructing the potential are further determined, and N-soliton solution of the mscmKdV equation is finally obtained. In addition, the one- and two-soliton solutions are shown to explore the characteristics of soliton dynamics in the mscmKdV equation. It is revealed from the mscmKdV equation that compared with the constant velocity and amplitude propagation of a soliton in the background of constant-coefficient isospectral model, one of the variable-coefficient isospectral systems propagates with variable velocity but constant amplitude, while for the case of non-spectrum, whether its coefficients are variable or not, soliton always propagates with variable velocity and amplitude.
  PubDate: 2023-10-01