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Similar Journals
 Nonlinear DynamicsJournal Prestige (SJR): 1.468 Citation Impact (citeScore): 4Number of Followers: 20      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1573-269X - ISSN (Online) 0924-090X Published by Springer-Verlag  [2658 journals]
• Spiking dynamics and synchronization properties of optical neurons based
on VCSEL-SAs

Abstract: We systematically investigate the spiking dynamics of optical neurons consisting of vertical-cavity surface emitting laser with an embedding saturable absorber (VCESL-SA) and the synchronization properties of coupled networks. The amplitude of spikes and the inter-spike interval of the spiking neurons are mainly considered. We also observe cluster synchronization in regular small networks that can be predicted via the adjacent matrix and further investigate the coherence in large-scale networks (up to a thousand nodes) with 4 typical typologies. Besides, the effect of a biologically observed autapse (which acts as a delayed self-feedback of an optical neuron) on the synchronization of network is taken into account. This work provides basic investigations of the spiking dynamics and synchronization properties in networks of coupled optical neurons in comparison of the fundamental researches based on biological neurons and neuron models, which may be helpful in potential implementations of optical neural networks that mimic the biological brains.
PubDate: 2021-07-19

• Normal form approach in the motion planning of space robots: a case study

Abstract: We examine applicability of normal forms of non-holonomic robotic systems to the problem of motion planning. A case study is analyzed of a planar, free-floating space robot consisting of a mobile base equipped with an on-board manipulator. It is assumed that during the robot’s motion its conserved angular momentum is zero. The motion planning problem is first solved at velocity level, and then torques at the joints are found as a solution of an inverse dynamics problem. A novelty of this paper lies in using the chained normal form of the robot’s dynamics and corresponding feedback transformations for motion planning at the velocity level. Two basic cases are studied, depending on the position of mounting point of the on-board manipulator. Comprehensive computational results are presented, and compared with the results provided by the Endogenous Configuration Space Approach. Advantages and limitations of applying normal forms for robot motion planning are discussed.
PubDate: 2021-07-19

• Dark wave, rogue wave and perturbation solutions of Ivancevic option
pricing model

Abstract: Under investigation in this paper is the Ivancevic option pricing model. Based on trial function method, rogue wave and dark wave solutions are constructed. By means of symbolic computation, these analytical solutions are obtained with the Maple. Perturbation solutions are obtained through direct perturbation method. These results will enrich the existing literature of the Ivancevic option pricing model. Dynamical characteristics for rogue waves and dark waves are exhibited by using three-dimensional plots, curve plots, density plots and contour plots.
PubDate: 2021-07-19

• Multi-soliton solutions of the N-component nonlinear Schrödinger
equations via Riemann–Hilbert approach

Abstract: In this paper, we utilize the Riemann–Hilbert approach to discuss multi-soliton solutions of the N-component nonlinear Schrödinger equations. Firstly, by transformed Lax pair, we construct the matrix-valued functions $$P_{1,2}$$ that satisfy the analyticity and normalization and the corresponding jump matrix can be determined. Then, in the reflectionless case, we get the multi-soliton solutions $$q_{l}$$ $$(l=1,\ldots ,N)$$ of the N-component nonlinear Schrödinger equations, which are related to the spectral parameter $$\eta$$ . Particularly, the 2-soliton solutions $$q_{1}$$ , $$q_{2}$$ , and $$q_{3}$$ of the three-component nonlinear Schrödinger equations are given and the corresponding 2-soliton diagrams are drawn.
PubDate: 2021-07-19

• Analysis of a new coupled hyperchaotic model and its topological types

Abstract: In order to construct the high-dimensional discrete hyperchaotic systems systemically, this paper proposes a new coupled chaotic model. It has a wide chaotic parameter range and can relax the election of the coupling coefficient. Sufficient conditions are derived to prove the existence of Li–Yorke chaos in the proposed model. Meanwhile, the existence of hyperchaos is also demonstrated. To discern the effects of different coupling types on the chaotic dynamics more comprehensively, we further explore the dynamical behaviors with various coupling structures by using Lyapunov spectrum, bifurcation analysis, and phase portraits. We investigate the interaction relationship between coupled units and give suggestions for selecting coupling types. The results indicate that the coupled model has more complex and more stable chaotic performance when there exists a loop in its topological structure. Further, synchronization is also discussed in this work; analysis results illustrate that the proposed model cannot be suppressed to periodic points at sufficiently high coupling strengths. This paper suggests an effective method that may contribute to studying hyperchaos design and coupled chaotic systems.
PubDate: 2021-07-19

• Nonlinear dynamic response of an isolation system with superelastic
hysteresis and negative stiffness

Abstract: The negative stiffness exhibited by bi-stable mechanisms together with the tunable superelasticity offered by shape memory alloy (SMA) wires can enhance the dynamic resilience of a structure in the context of vibration isolation. The effects of negative stiffness and superelastic damping in base-isolated structures are here explored by carrying out an extensive study of the nonlinear dynamic response via pathfollowing, bifurcation analysis, and time integration. The frequency-response curves of the isolated structure, with and without the negative stiffness contribution, are numerically obtained for different excitation amplitudes to construct the acceleration and displacement transmissibility curves. The advantages of negative stiffness, such as damping augmentation and reduced acceleration/displacement transmissibility, as well as the existence of rich bifurcation scenarios toward quasi-periodicity and chaos, are discussed.
PubDate: 2021-07-18

• A magnetic control method for large-deformation vibration of cantilevered
pipe conveying fluid

Abstract: Soft active materials have the ability to undergo large deformation in response to stimuli such as light, heat, magnetic, and electric fields. Due to their promising applications in the fields of soft robots, flexible electronics, and biomedicine engineering, they have attracted tremendous attention from different disciplines and developed rapidly in the past decades basing on mutual efforts. Recently, a new class of soft active materials, known as hard-magnetic soft (HMS) materials is successfully developed. By applying magnetic fields, unprecedented mechanical behaviors of HMS structures have been observed. To further explore the potential applications of HMS materials, this work will investigate the dynamical behaviors of fluid-conveying pipes made of HMS materials for the first time. By considering the exactly geometric nonlinearities due to the bending deformation of the pipe, the governing equation of a cantilevered HMS pipe conveying fluid is derived based on Hamilton’s principle. The analyses of the stability, static deformation, and nonlinear vibration of the HMS pipe are conducted by solving the obtained governing equation. It is found that there is a critical flow velocity for the dynamic instability of the pipe. When the flow velocity is below this value, the HMS pipe may undergo a large static deformation in a stable state. However, the pipe would periodically oscillate with a large amplitude when the flow velocity is beyond the critical flow velocity. Results also indicate the mechanical responses including static deformation, loss of stability, and vibration of the HMS pipe conveying fluid can be effectively controlled by applying an external magnetic field.
PubDate: 2021-07-17

• Distributed output feedback leader-following consensus for nonlinear
multiagent systems with time delay

Abstract: This paper concentrates on the output feedback control problem for a class of nonlinear multiagent systems governed by the high-order strict-feedback model with time delay. Within the dynamic gain technique and the Lyapunov-like method, the dynamic gain state observer for each agent is put forward with the hope to compensate the impact induced by the immeasurable state variables, and then the distributed leader-following consensus protocols which are independent of the time delay on the agent state are designed such that the output of each follower can asymptotically track that of the leader. Besides, the problem considered is extended into the general case where the Lipschitz growth rates of the nonlinear function are unknown time-varying functions. Finally, simulation examples are performed to illustrate the validity and effectiveness of the proposed approach.
PubDate: 2021-07-15

• Adaptive event-triggered control for nonlinear multi-agent systems with
unknown control directions and actuator failures

Abstract: This paper presents an event-triggered adaptive consensus algorithm to deal with the consensus problem for nonlinear multi-agent systems (MASs) with unknown control direction and actuator failures. The nonlinear dynamics and the disturbance considered in this paper are all unknown. The unknown nonlinear dynamics of MASs is approximated by the radial basis function neural networks (RBFNNs). Then, a disturbance observer with adaptive parameter is put forward to depress the total disturbances which contain the unknown external disturbances, RBFNNs approximation errors and bias faults. The proposed consensus algorithm enables that all closed-loop signals are bounded, and the followers’ states can track the leader’s. Finally, the proposed consensus algorithm is validated by simulations.
PubDate: 2021-07-15

• Inherent anti-interference in fractional-order autonomous coupled
resonator

Abstract: Coupled resonator is one of the fundamental physical systems, which has always been modeled by integer-order calculus or composed of integer-order components. To achieve wider operating area of low power consumption, the energy distribution of coupled resonator is often expected to be robust. However, the energy distribution is susceptible to the interference of resonator parameters shifting in real world, such as coupling strength and resonator frequency. Traditionally, the anti-interference ability of integer-order coupled resonator can be acquired by using externally and additionally complicated control. Here, we report an alternative fractional-order autonomous coupled resonator, in which the anti-interference ability can inherently arise through its fractional-order nature. By using the equivalent coupling circuit of fractional-order autonomous coupled resonator, its energy characteristics are analyzed. Moreover, we theoretically find and experimentally prove that the energy distribution of the fractional-order coupled resonator could be locked by the order of fractional-order element. Our work could help coupled resonator acquire unprecedented anti-interference ability.
PubDate: 2021-07-15

• The N-level (N ≥ 4) logistic cascade homogenized mapping
for image encryption

Abstract: This paper proposed a chaotic system of N-level logistic cascaded homogenization mapping (N-LLCHM). The cascade structure of multiple one-dimensional logistic mappings results in an exponential increase in the number of fixed points in the mapping, which greatly increases the initial error divergence of the system during the iteration process, and ultimately increases the complexity of the system to generate time series. In the experiment, the homogenization adjustment function of the mapping is derived according to the maximum entropy theorem. The homogenization adjustment function and the N-level logistic cascade structure are cascaded again to construct a complete dynamics system. The analyses of indicators such as information entropy, Lyapunov exponent, spectral entropy and NIST SP800-22 randomness test reveal that the mapping generates a chaotic time series with good aperiodic and uniform distribution characteristics under the condition that N is greater than or equal to 4. Then, N-LLCHM is used as the core of pseudo-random number generator, and the color image encryption algorithm is constructed by using three steps of pixel bidirectional cross-coding, position scrambling and pixel diffusion as the main system. According to the evaluation of histogram, correlation, information entropy and anti-differential attack test, it is verified that this algorithm has better encryption effect and higher security than the present image encryption algorithms.
PubDate: 2021-07-14

• Shifts in control parameter dynamically access individual attractors in a
multistable system

Abstract: We propose a technique called the power-shift method to discover new attractors and access known attractors in experimental systems by solely shifting the control parameter of a multistable system in situ. Power shifting is a type of incremental perturbation of the control parameter that allows the system to be placed in an otherwise difficult-to-access attractor by using other attractors as steppingstones. We find that by power shifting within certain time windows of the limit cycle, we can reliably access a desired attractor. The power-shift method is demonstrated theoretically with noise using a single-mode coherent model of a laser with injected signal.
PubDate: 2021-07-14

• Correction to: New theories and applications of tempered fractional
differential equations

PubDate: 2021-07-13

• Mean-square stability of the zero equilibrium of the nonlinear delay
differential equation: Nicholson’s blowflies application

Abstract: We are concerned about the stochastic nonlinear delay differential equation. The stochasticity arises from the white Gaussian noise, which is the time derivative of the standard Brownian motion. The main objective of this paper is to introduce a new technique using the Lyapunov functional for the study of stability of the zero solution of the stochastic delay differential system. Constructing a new appropriate deterministic system in the neighborhood of the origin is an effective way to investigate the necessary and sufficient conditions of stability in the sense of the mean square. Nicholson’s blowflies equation is one of the major problems in ecology; necessary conditions for the possible extinction of the Nicholson’s blowflies population are investigated. We support our theoretical results by providing areas of stability and some numerical simulations of the solution of the system using the Euler–Maruyama scheme, which is mean square stable Maruyama (Rendiconti del Circolo Matematico di Palermo 4(1):48, 1955), Cao et al. (Appl Math Comput 159(1):127–135, 2004).
PubDate: 2021-07-13

• Nonlinear vibrations of rotating pretwisted composite blade reinforced by
functionally graded graphene platelets under combined aerodynamic load and
airflow in tip clearance

Abstract: The primary resonance and nonlinear vibrations of the functionally graded graphene platelet (FGGP)-reinforced rotating pretwisted composite blade under combined the external and multiple parametric excitations are investigated with three different distribution patterns. The FGGP-reinforced rotating pretwisted composite blade is simplified to the rotating pretwisted composite cantilever plate reinforced by the functionally graded graphene platelet. It is novel to simplify the leakage of the airflow in the tip clearance to the non-uniform axial excitation. The rotating speed of the steady state adding a small periodic perturbation is considered. The aerodynamic load subjecting to the surface of the plate is simulated as the transverse excitation. Utilizing the first-order shear deformation theory, von Karman nonlinear geometric relationship, Lagrange equation and mode functions satisfying the boundary conditions, three-degree-of-freedom nonlinear ordinary differential equations of motion are derived for the FGGP-reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations. The primary resonance and nonlinear dynamic behaviors of the FGGP-reinforced rotating pretwisted composite cantilever plate are analyzed by Runge–Kutta method. The amplitude–frequency response curves, force–frequency response curves, bifurcation diagrams, maximum Lyapunov exponent, phase portraits, waveforms and Poincare map are obtained to investigate the nonlinear dynamic responses of the FGGP-reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations.
PubDate: 2021-07-13

• Adaptive neural consensus tracking control for multi-agent systems with
unknown state and input hysteresis

Abstract: An indirect adaptive consensus control method is presented for multi-agent systems (MASs) with unknown hysteresis states and input. All system states that can be utilized to design the controller are measured by the sensors subjected to hysteresis, and thus, the system state values are inaccurate. Meanwhile, it is difficult to compensate the input hysteresis for it is coupled with the state hysteresis. The unknown function from agent’s neighbors also increases the difficulty of controller design. To eliminate the influence of unknown input hysteresis, an inverse adaptive compensated method is presented. The problem of state hysteresis is addressed by designing two adaptive laws to approximate the upper and lower bounds of unknown hysteresis coefficient. Neural networks are introduced to handle the unknown dynamics of agent and its neighbors. The proposed control scheme can guarantee that the consensus errors of followers converge to a predefined interval of zero asymptotically. In addition, the transient performance of MASs can be further ensured. The simulation examples are included to verify the effectiveness of the presented control approach.
PubDate: 2021-07-12

• Model order reduction based on direct normal form: application to large
finite element MEMS structures featuring internal resonance

Abstract: Dimensionality reduction in mechanical vibratory systems poses challenges for distributed structures including geometric nonlinearities, mainly because of the lack of invariance of the linear subspaces. A reduction method based on direct normal form computation for large finite element (FE) models is here detailed. The main advantage resides in operating directly from the physical space, hence avoiding the computation of the complete eigenfunctions spectrum. Explicit solutions are given, thus enabling a fully non-intrusive version of the reduction method. The reduced dynamics is obtained from the normal form of the geometrically nonlinear mechanical problem, free of non-resonant monomials, and truncated to the selected master coordinates, thus making a direct link with the parametrisation of invariant manifolds. The method is fully expressed with a complex-valued formalism by detailing the homological equations in a systematic manner, and the link with real-valued expressions is established. A special emphasis is put on the treatment of second-order internal resonances and the specific case of a 1:2 resonance is made explicit. Finally, applications to large-scale models of micro-electro-mechanical structures featuring 1:2 and 1:3 resonances are reported, along with considerations on computational efficiency.
PubDate: 2021-07-11

• Stability enhancement optimization method for suppressing speed
fluctuation under large-scale speed regulation process of super-high-speed
electric air compressor

Abstract: As a core component of fuel cell systems, a super-high-speed electric air compressor plays a decisive role in effective operation of fuel cell system. A super-high-speed electric air compressor must have high speed and high response abilities. At the same time, super-high-speed electric air compressor should have lower speed fluctuations in order to prevent excessive pressure pulsation damage to the stack. To solve this problem, firstly, mathematical model of super-high-speed electric air compressor is established considering rotation dynamics. Secondly, considering the influence of load torque on system dynamics, Hopf bifurcation theory is used to reveal influence of the load torque on the stability domain of voltage reference. Finally, according to the results of dynamic theory analysis, a stability enhancement optimization method is proposed, and controller design of the air compressor is carried out. The obtained results show that the proposed method effectively suppresses speed fluctuations in the process of large-scale speed regulation.
PubDate: 2021-07-09

• Chaos for communication

Abstract: This work shows that chaotic signals with different power spectrum and different positive Lyapunov exponents are robust to linear superposition, meaning that the superposition preserves the Lyapunov exponents and the information content of the source signals, even after being transmitted over non-ideal physical medium. This work tackles with great detail how chaotic signals and their information content are affected when travelling through medium that presents the non-ideal properties of multi-path propagation, noise and chaotic interference (linear superposition), and how this impacts on the proposed communication system. Physical media with other non-ideal properties (dispersion and interference with periodic signals) are also discussed. These wonderful properties that chaotic signals have allow me to propose a novel communication system based on chaos, where information composed from and to multiple users each operating with different base frequencies and that is carried by chaotic wavesignals, can be fully preserved after transmission in the open air wireless physical medium, and it can be trivially decoded with low probability of errors.
PubDate: 2021-07-09

• Fixed-time synchronization of inertial complex-valued neural networks with
time delays

Abstract: This paper studies the problem of fixed-time synchronization for a class of delayed complex-valued neural networks with inertial term. Two different controllers are designed, under which the addressed inertial complex-valued neural networks with different types of activation functions can achieve synchronization perfectly in a fixed time. The corresponding synchronization criteria in terms of matrix inequalities and the estimates of the settling times are derived by using separation and direct methods, respectively, which are concise and easy to verify compared with algebraic inequalities conditions. Some innovative inequalities in the complex field are fully utilized. The in-depth analysis results are an advancement of the existing research progress. Finally, in order to support the theoretical results, numerical simulations for different types of activation functions are provided.
PubDate: 2021-07-09

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