scholarly journals A THREE-DIMENSIONAL NONLINEAR SYSTEM WITH A SINGLE HETEROCLINIC TRAJECTORY

2020 ◽  
Vol 10 (1) ◽  
pp. 249-266 ◽  
Author(s):  
Xianyi Li ◽  
◽  
Haijun Wang
Keyword(s):  
Nonlinear System ◽  
Three Dimensional ◽  
Heteroclinic Trajectory

scholarly journals A mathematical model of infectious disease transmission

2020 ◽  
Vol 34 ◽  
pp. 02002
Author(s):  
Aurelia Florea ◽  
Cristian Lăzureanu
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Nonlinear System ◽  
Numerical Simulations ◽  
Disease Transmission ◽  
Three Dimensional ◽  
Type System ◽  
Epidemic Disease ◽  
Infectious Disease Transmission ◽  
The Stability

In this paper we consider a three-dimensional nonlinear system which models the dynamics of a population during an epidemic disease. The considered model is a SIS-type system in which a recovered individual automatically becomes a susceptible one. We take into account the births and deaths, and we also consider that susceptible individuals are divided into two groups: non-vaccinated and vaccinated. In addition, we assume a medical scenario in which vaccinated people take a special measure to quarantine their newborns. We study the stability of the considered system. Numerical simulations point out the behavior of the considered population.

scholarly journals The Dynamic Three-Dimensional Localization of Fields in Active Percolating Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Gennadiy Burlak
Keyword(s):  
Fractal Dimension ◽  
Nonlinear System ◽  
Three Dimensional ◽  
Percolation Cluster ◽  
Localized States ◽  
3D Simulations ◽  
Localized Solutions ◽  
Anisotropic Inhomogeneity

We study a dynamic three-dimensional (3D) field localized states in a medium with percolation disorder, where the percolation cluster is filled by the active nanoemitters. In such a system, the incipient percolating cluster generates a fractal radiating structure in which the field is radiated and scattered by the anisotropic inhomogeneity. Our numerical 3D simulations show that such a nonlinear system with noninteger fractal dimension has well-defined localized solutions for fields (3D speckles). The statistics of speckles is studied too.

Takagi–Sugeno Fuzzy Predictive Control for a Class of Nonlinear System With Constrains and Disturbances

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Bin Wang ◽  
Jianwei Zhang ◽  
Delan Zhu ◽  
Diyi Chen
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Predictive Control ◽  
Three Dimensional ◽  
Fuzzy Model ◽  
Control Input ◽  
Chen System ◽  
External Disturbances ◽  
Takagi Sugeno ◽  
Fuzzy Predictive Control

This paper investigates the fuzzy predictive control for a class of nonlinear system with constrains under the condition of noise. Based on the fuzzy linearization theory, a class of nonlinear systems can be described by the Takagi–Sugeno (T–S) fuzzy model. The T–S fuzzy model and predictive control are combined to stabilize the proposed class of nonlinear system, and the detailed mathematical derivation is given. Moreover, the designed controller has been optimized even if the system is constrained by output and control input, or perturbed by external disturbances. Finally, numerical simulations including three-dimensional Lorenz system, four-dimensional Chen system and five-dimensional nonlinear system with external disturbances are presented to demonstrate the universality and effectiveness of the proposed scheme. The approach proposed in this paper is simple and easy to implement and also provides reference for relevant nonlinear systems.

scholarly journals Numerical Treatment for the Three-Dimensional Eyring-Powell Fluid Flow over a Stretching Sheet with Velocity Slip and Activation Energy

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad Umar ◽  
Rizwan Akhtar ◽  
Zulqurnain Sabir ◽  
Hafiz Abdul Wahab ◽  
Zhu Zhiyu ◽  
...  
Keyword(s):  
Activation Energy ◽  
Nonlinear System ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Lewis Number ◽  
Velocity Slip ◽  
Dynamical Analysis ◽  
Physical Parameters ◽  
Similarity Transformations ◽  
Computational Paradigm

In this manuscript, a computational paradigm of technique shooting is exploited for investigation of the three-dimensional Eyring-Powell fluid with activation energy over a stretching sheet with slip arising in the field of fluid dynamics. The problem is modeled and resulting nonlinear system of PDEs is transformed into nonlinear system of ODEs using well-known similarity transformations. The strength of shooting based computing approach is employed to analyze the dynamics of the system. The proposed technique is well-designed for different scenarios of the system based on three-dimensional non-Newtonian fluid with activation energy over a stretching sheet. Slip condition is also incorporated to enhance the physical and dynamical analysis of the system. The proposed results are compared with the bvp4C method for the correctness of the solver. Graphical and numerical illustrations are used to envisage the behavior of different proficient physical parameters of interest including magnetic parameter, stretching rate parameter, velocity slip parameter, Biot number on velocity, and Lewis number on temperature and concentration.

scholarly journals The Application of the Undetermined Fundamental Frequency Method on the Period-Doubling Bifurcation of the 3D Nonlinear System

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Gen Ge ◽  
Wei Wang
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Fundamental Frequency ◽  
Three Dimensional ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Cubic Nonlinearity ◽  
Frequency Method ◽  
The Stability ◽  
Second Period

The analytical method to predict the period-doubling bifurcation of the three-dimensional (3D) system is improved by using the undetermined fundamental frequency method. We compute the stable response of the system subject to the quadratic and cubic nonlinearity by introducing the undetermined fundamental frequency. For the occurrence of the first and second period-doubling bifurcation, the new bifurcation criterion is accomplished. It depends on the stability of the limit cycle on the central manifold. The explicit applications show that the new results coincide with the results of the numerical simulation as compared with the initial methods.

scholarly journals The Dynamic Evaluation of Tilted Support Spring Nonlinear System with Critical Components under the Action of a Rectangular Pulse

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ningning Duan ◽  
Shuang Song ◽  
Anjun Chen
Keyword(s):  
Nonlinear System ◽  
Pulse Duration ◽  
Frequency Ratio ◽  
Three Dimensional ◽  
Response Spectra ◽  
Rectangular Pulse ◽  
Numerical Results ◽  
Dynamical Equations ◽  
Shock Response ◽  
Critical Components

Dimensionless nonlinear dynamical equations of a tilted support spring nonlinear system with critical components were obtained under the action of a rectangular pulse, and the numerical results of the shock response were studied using Runge-Kutta method. To evaluate the dynamic characteristics of critical components, a new concept of three-dimensional shock response spectra was proposed, where the ratio of the maximum shock response acceleration of critical components to the peak pulse acceleration, the pulse duration, and the frequency ratio were three basic parameters of three-dimensional shock response spectra. Based on the numerical results, the effects of the angle, the peak pulse acceleration, the mass ratio, the frequency ratio, and the pulse duration on the shock response spectra were discussed.

scholarly journals Fixed-time Adaptive Control for A New Three-dimensional Nonlinear System with Circular Equilibrium

2020 ◽  
Vol 1626 ◽  
pp. 012095
Author(s):  
Yaoyu Wang ◽  
Ling Liu ◽  
Xinshan Cai ◽  
Chongxin Liu ◽  
Yan Wang
Keyword(s):  
Adaptive Control ◽  
Nonlinear System ◽  
Three Dimensional ◽  
Fixed Time

The Reachable set of a Three-Dimensional Nonlinear System Describing Sewage Treatment

2016 ◽  
Vol 27 (3) ◽  
pp. 275-289
Author(s):  
N. V. Bondarenko ◽  
E’. V. Grigor’eva ◽  
E. N. Khailov
Keyword(s):  
Nonlinear System ◽  
Sewage Treatment ◽  
Three Dimensional ◽  
Reachable Set
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