A Sequential Order of Periodic Motions in a 1-Dimensional, Time-Delay, Dynamical System

2020 ◽  
pp. 95-112
Author(s):  
Siyuan Xing ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical System ◽  
Time Delay ◽  
Periodic Motions ◽  
Sequential Order ◽  
Delay Dynamical System

TWO-SCROLL ATTRACTOR IN A DELAY DYNAMICAL SYSTEM

2007 ◽  
Vol 17 (10) ◽  
pp. 3455-3460 ◽  
Author(s):  
ARŪNAS TAMAŠEVIČIUS ◽  
TATJANA PYRAGIENĖ ◽  
MANTAS MEŠKAUSKAS
Keyword(s):  
Dynamical System ◽  
Time Delay ◽  
Nonlinear Function ◽  
Delay System ◽  
The Novel ◽  
Type Function ◽  
Delay Dynamical System ◽  
Glass Type ◽  
Electronic Oscillator

Nonvanishing 𐑍-shaped nonlinear function has been introduced in delay dynamical system instead of commonly used Mackey–Glass type function. Depending on time delay the system exhibits not only mono-scroll, but also more complex two-scroll hyperchaotic attractors. Delay system with the novel nonlinear function can be implemented as an analogue electronic oscillator.

scholarly journals The reproductive number R0 of COVID-19 based on estimate of a statistical time delay dynamical system

2020 ◽  
Author(s):  
Nian Shao ◽  
Jin Cheng ◽  
Wenbin Chen
Keyword(s):  
Dynamical System ◽  
Growth Rate ◽  
Time Delay ◽  
Dynamic System ◽  
Reproductive Number ◽  
Generation Interval ◽  
Delay Dynamical System ◽  
Simulation Results ◽  
Statistical Time

AbstractIn this paper, we estimate the reproductive number R0 of COVID-19 based on Wallinga and Lipsitch framework [11] and a novel statistical time delay dynamic system. We use the observed data reported in CCDC’s paper to estimate distribution of the generation interval of the infection and apply the simulation results from the time delay dynamic system as well as released data from CCDC to fit the growth rate. The conclusion is: Based our Fudan-CCDC model, the growth rate r of COVID-19 is almost in [0.30, 0.32] which is larger than the growth rate 0.1 estimated by CCDC [9], and the reproductive number R0 of COVID-19 is estimated by 3.25 ≤ R0 ≤ 3.4 if we simply use R = 1 + r ∗ Tc with Tc = 7.5, which is bigger than that of SARS. Some evolutions and predictions are listed.

scholarly journals A time delay dynamical model for outbreak of 2019-nCoV and the parameter identification

2020 ◽  
Vol 28 (2) ◽  
pp. 243-250 ◽  
Author(s):  
Yu Chen ◽  
Jin Cheng ◽  
Yu Jiang ◽  
Keji Liu
Keyword(s):  
Dynamical System ◽  
Time Delay ◽  
Parameter Identification ◽  
Typical Feature ◽  
The Novel ◽  
Isolation Rate ◽  
High Isolation ◽  
The Government ◽  
System With Time Delay ◽  
Official Data

AbstractIn this paper, we propose a novel dynamical system with time delay to describe the outbreak of 2019-nCoV in China. One typical feature of this epidemic is that it can spread in the latent period, which can therefore be described by time delay process in the differential equations. The accumulated numbers of classified populations are employed as variables, which is consistent with the official data and facilitates the parameter identification. The numerical methods for the prediction of the outbreak of 2019-nCoV and parameter identification are provided, and the numerical results show that the novel dynamic system can well predict the outbreak trend so far. Based on the numerical simulations, we suggest that the transmission of individuals should be greatly controlled with high isolation rate by the government.

Control of multi-scroll attractors in a memristor-coupled resonator via time-delayed feedback

2018 ◽  
Vol 32 (32) ◽  
pp. 1850399 ◽  
Author(s):  
Zhilong Liu ◽  
Fuqiang Wu ◽  
Faris Alzahrani ◽  
Jun Ma
Keyword(s):  
Dynamical System ◽  
Time Delay ◽  
Magnetic Flux ◽  
Memory Effect ◽  
Delayed Feedback ◽  
Feedback Gain ◽  
Initial Setting ◽  
Physical Background ◽  
Time Delayed Feedback ◽  
With Memory

A four-variable dynamical system composed of memristor is proposed to investigate the dependence of multi-scroll attractor on initial setting for one variable with memory, and the description for physical background is supplied. It is found that appropriate setting of initial values for the memory variable can induce different numbers of attractor, as a result, resetting initials can change the profile of attractors which is also dependent on the calculating period. Time-delayed feedback is used to stabilize the dynamical system thus the effect of initial dependence is suppressed and multi-scroll attractors are controlled by applying appropriate time delay and feedback gain in the controller. Furthermore, the system is verified on FPGA circuit platform and memristor is used to describe the memory effect of variable related to magnetic flux. It is confirmed that multi-scroll attractors can be stabilized and the dependence of initials setting is suppressed in experiment way.

Dynamics of Neural Networks as Nonlinear Systems with Several Equilibria

2011 ◽  
pp. 331-357 ◽  
Author(s):  
Daniela Danciu
Keyword(s):  
Neural Network ◽  
Dynamical System ◽  
Neural Networks ◽  
Time Delay ◽  
Dynamical Systems ◽  
Qualitative Properties ◽  
The Neural Network ◽  
The Neural Networks ◽  
Global Asymptotics ◽  
Dynamical Properties

Neural networks—both natural and artificial, are characterized by two kinds of dynamics. The first one is concerned with what we would call “learning dynamics”. The second one is the intrinsic dynamics of the neural network viewed as a dynamical system after the weights have been established via learning. The chapter deals with the second kind of dynamics. More precisely, since the emergent computational capabilities of a recurrent neural network can be achieved provided it has suitable dynamical properties when viewed as a system with several equilibria, the chapter deals with those qualitative properties connected to the achievement of such dynamical properties as global asymptotics and gradient-like behavior. In the case of the neural networks with delays, these aspects are reformulated in accordance with the state of the art of the theory of time delay dynamical systems.

On Time-Delay Effects on Period-1 Motions in a Periodically Forced, Time-Delayed, Duffing Oscillator

2016 ◽  
Author(s):  
Albert C. J. Luo ◽  
Siyuan Xing
Keyword(s):  
Time Delay ◽  
Analytical Solutions ◽  
Analytical Method ◽  
Duffing Oscillator ◽  
Delay Systems ◽  
Harmonic Amplitude ◽  
Time Delay Systems ◽  
Periodic Motions ◽  
Delay Effects ◽  
The Stability

In recent decades, nonlinear time-delay systems were often applied in controlling nonlinear systems, and the stability of such time-delay systems was very actively discussed. Recently, one was very interested in periodic motions in nonlinear time-delay systems. Especially, the semi-analytical solutions of periodic motions in time-delay systems are of great interest. From the semi-analytical solutions, the nonlinearity and complexity of periodic motions in the time-delay systems can be discussed. In this paper, time-delay effects on periodic motions of a periodically forced, damped, hardening, Duffing oscillator are analytically discussed through a semi-analytical method. The semi-analytical method is based on discretization of the differential equation of such a Duffing oscillator to obtain the corresponding implicit discrete mappings. Through such implicit mappings and mapping structures of periodic motions, period-1 motions varying with time-delay are discussed, and the corresponding stability and bifurcation analysis of periodic motions are carried out through eigenvalue analysis. Numerical results of periodic motions are illustrated to verify analytical predictions. The corresponding harmonic amplitude spectrums and harmonic phases are presented for a better understanding of periodic motions in such a nonlinear oscillator.

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