scholarly journals An Initial-Controlled Double-Scroll Hyperchaotic Map

2021 ◽  
Author(s):  
Yongxin Li ◽  
Chunbiao Li ◽  
Sicong Liu ◽  
Tengfei Lei ◽  
Yicheng Jiang
Keyword(s):  
Dynamical System ◽  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Initial Condition ◽  
Offset Boosting ◽  
Sine Functions ◽  
Sinusoidal Function

Abstract Initial condition-dominated offset boosting provides a special channel to arrange coexisting orbits. Due to the nonlinearity and inherent periodicity, sinusoidal function is often introduced into a dynamical system for multistability design. In this paper, an initial-controlled double-scroll hyperchaotic map is constructed based on two sine functions. Four patterns of the double-scroll hyperchaotic orbits are found as 0-degree, 90-degree, 45-degree and 135-degree. Consequently, different modes for attractor growing are demonstrated. Finally, hardware experiments based on STM32 are carried out to verify the theoretical analysis and numerical simulation.

scholarly journals Asymmetry Evolvement and Controllability of a Symmetric Hyperchaotic Map

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1039
Author(s):  
Sixiao Kong ◽  
Chunbiao Li ◽  
Haibo Jiang ◽  
Yibo Zhao ◽  
Yanling Wang
Keyword(s):  
Numerical Simulation ◽  
Hardware Implementation ◽  
Trigonometric Function ◽  
Initial Condition ◽  
Trigonometric Functions ◽  
Negative Coefficient ◽  
Offset Boosting

Trigonometric functions were used to construct a 2-D symmetrical hyperchaotic map with infinitely many attractors. The regime of multistability depends on the periodicity of the trigonometric function, which is closely related to the initial condition. For this trigonometric nonlinearity and the introduction of an offset controller, the initial condition triggers a specific multistability evolvement, in which infinitely countless symmetric and asymmetric attractors are produced. Initial condition-triggered offset boosting is explored, combined with constant controlled offset regulation. Furthermore, this symmetric map gives the sequences in various types of asymmetric attractors, in which the polarity balance is maintained by the initial condition and a negative coefficient due to the trigonometric function. Finally, as determined through the hardware implementation of STM32, the corresponding results agree with the numerical simulation.

scholarly journals Multivalued Discrete Tomography Using Dynamical System That Describes Competition

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Takeshi Kojima ◽  
Tetsushi Ueta ◽  
Tetsuya Yoshinaga
Keyword(s):  
Dynamical System ◽  
Theoretical Analysis ◽  
Continuous Time ◽  
Numerical Experiments ◽  
Nonlinear Dynamical System ◽  
Reconstructed Image ◽  
Optimization Approach ◽  
Discrete Tomography ◽  
Nonlinear Dynamical ◽  
Time Optimization

Multivalued discrete tomography involves reconstructing images composed of three or more gray levels from projections. We propose a method based on the continuous-time optimization approach with a nonlinear dynamical system that effectively utilizes competition dynamics to solve the problem of multivalued discrete tomography. We perform theoretical analysis to understand how the system obtains the desired multivalued reconstructed image. Numerical experiments illustrate that the proposed method also works well when the number of pixels is comparatively high even if the exact labels are unknown.

Vibrational Resonance in an Overdamped System with a Fractional Order Potential Nonlinearity

2018 ◽  
Vol 28 (07) ◽  
pp. 1850082 ◽  
Author(s):  
Jianhua Yang ◽  
Dawen Huang ◽  
Miguel A. F. Sanjuán ◽  
Houguang Liu
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Low Frequency ◽  
Response Amplitude ◽  
Resonance Phenomenon ◽  
Vibrational Resonance ◽  
Frequency Excitation ◽  
Overdamped System

We investigate the vibrational resonance by the numerical simulation and theoretical analysis in an overdamped system with fractional order potential nonlinearities. The nonlinearity is a fractional power function with deflection, in which the response amplitude presents vibrational resonance phenomenon for any value of the fractional exponent. The response amplitude of vibrational resonance at low-frequency is deduced by the method of direct separation of slow and fast motions. The results derived from the theoretical analysis are in good agreement with those of numerical simulation. The response amplitude decreases with the increase of the fractional exponent for weak excitations. The amplitude of the high-frequency excitation can induce the vibrational resonance to achieve the optimal response amplitude. For the overdamped systems, the nonlinearity is the crucial and necessary condition to induce vibrational resonance. The response amplitude in the nonlinear system is usually not larger than that in the corresponding linear system. Hence, the nonlinearity is not a sufficient factor to amplify the response to the low-frequency excitation. Furthermore, the resonance may be also induced by only a single excitation acting on the nonlinear system. The theoretical analysis further proves the correctness of the numerical simulation. The results might be valuable in weak signal processing.

Theoretical Analysis and Numerical Simulation of Laser to Rock

2008 ◽  
Vol 35 (8) ◽  
pp. 1245-1249 ◽  
Author(s):  
李密 Li Mi ◽  
王岩楼 Wang Yanlou ◽  
王亚丽 Wang Yali ◽  
张传绪 Zhang Chuanxu ◽  
刘军 Liu Jun
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis

scholarly journals Nonsingular PNG-Based Impact Time Control Guidance with Lower Dependence on Time-to-Go Estimate

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Sijiang Chang ◽  
Shengfu Chen
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Research Literature ◽  
Proportional Navigation ◽  
Impact Time ◽  
Time Control ◽  
Practical Engineering ◽  
Adjustable Range ◽  
Natural Characteristics ◽  
Proportional Navigation Guidance

In a bid to take advantage of natural characteristics of the proportional navigation guidance (PNG) in practical engineering, the PNG-based impact time control guidance (ITCG) continues to be a popular alternative for achieving the desired impact time of a missile. For most such ITCG, the performance is dependent on the accuracy of the time-to-go estimation. Along the lines of the development of PNG-based ITCG in earlier studies, a nonsingular ITCG is proposed on the basis of nonlinear formulations. It is demonstrated that, by theoretical analysis and numerical simulation, this proposed ITCG is shown to be advantageous in certain circumstances. By deriving a novel additional acceleration command, the proposed law is of lower dependence on time-to-go estimate and is capable of eliminating some singularities, leading to wider adjustable range of the desired impact time and better adaptability to more conditions. This research is expected to be supplementary to those presented in the current research literature.

Sign in / Sign up

Export Citation Format

Share Document