5. Hyperbolic rest point and hyperbolic closed trajectory

2019 ◽  
pp. 66-76
Keyword(s):  
Closed Trajectory ◽  
Rest Point

Non-Attractive Periodic Trajectory Formation Mechanism on Random and Chaotic Time Series

2020 ◽  
Author(s):  
Hitoaki Yoshida ◽  
Takeshi Murakami
Keyword(s):  
Time Series ◽  
Formation Mechanism ◽  
Random Number ◽  
Periodic Trajectory ◽  
Closed Trajectory ◽  
Number Series ◽  
Pseudo Random Number ◽  
Trajectory Formation ◽  
Random Neural Network ◽  
Iot Devices

Pseudo-random number series extracted from chaotic and random time series from the chaotic and random neural network (CRNN) with fixed-point arithmetic has been the focus of attention for protecting the information security of IoT devices. Pseudo-random number series generated by a computer is eventually periodic, practically. The produced closed trajectory is not a limit cycle, because which does not divide the phase space into 2 regions. The closed trajectory in this work is called a non-attractive periodic trajectory (NPT) because it hardly attracts trajectories within the neighborhood. The method of preventing the closed trajectory formation has been proposed on the basis of the NPT formation mechanism in this paper. The method has extended the period of NPT considerably. It is expected to apply security applications for IoT devices.

A new 3-D chaotic jerk system with a saddle-focus rest point at the origin, its active backstepping control, and circuit realization

2021 ◽  
pp. 95-114
Author(s):  
Aceng Sambas ◽  
Sundarapandian Vaidyanathan ◽  
Sen Zhang ◽  
Mohamad Afendee Mohamed ◽  
Yicheng Zeng ◽  
...  
Keyword(s):  
Backstepping Control ◽  
Circuit Realization ◽  
Rest Point ◽  
Jerk System

scholarly journals Rest point theorems for autonomous control systems

1977 ◽  
Vol 58 (1) ◽  
pp. 98-112 ◽  
Author(s):  
M.L.J Hautus ◽  
Michael Heymann ◽  
Ronald J Stern
Keyword(s):  
Control Systems ◽  
Autonomous Control ◽  
Rest Point

scholarly journals FOUR–DIMENSIONAL BRUSSELATOR MODEL WITH PERIODICAL SOLUTION

2020 ◽  
Vol 6 (1) ◽  
pp. 3
Author(s):  
Odiljon S. Akhmedov ◽  
Abdulla A. Azamov ◽  
Gafurjan I. Ibragimov
Keyword(s):  
Dynamical System ◽  
Chemical Reactions ◽  
Main Property ◽  
External Source ◽  
Closed Trajectory ◽  
Dimensional Model ◽  
Tracking Method ◽  
Positive Orthant ◽  
Brusselator Model ◽  
Periodical Solution

In the paper, a four-dimensional model of cyclic reactions of the type Prigogine's Brusselator is considered. It is shown that the corresponding dynamical system does not have a closed trajectory in the positive orthant that will make it inadequate with the main property of chemical reactions of Brusselator type. Therefore, a new modified Brusselator model is proposed in the form of a four-dimensional dynamic system. Also, the existence of a closed trajectory is proved by the DN-tracking method for a certain value of the parameter which expresses the rate of addition one of the reagents to the reaction from an external source.

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