Mercury’s chaotic orbit poses no threat to Earth, says study

Physics Today ◽  
2015 ◽  
Keyword(s):  
Chaotic Orbit

Research on Weak Signal Amplification Principle Based on Parabola Map

2010 ◽  
Vol 139-141 ◽  
pp. 1963-1966
Author(s):  
Zhen Qiang Huang ◽  
Wen Li Zhao ◽  
Zhi Gang Wang
Keyword(s):  
Signal Amplification ◽  
Initial Conditions ◽  
Signal To Noise Ratio ◽  
Weak Signal ◽  
Initial Value ◽  
Chaotic Orbit ◽  
Advantages And Disadvantages ◽  
Useful Signal ◽  
Nonlinear Amplification ◽  
The One

In this paper, a new nonlinear amplification principle based on chaotic theory is proposed. Firstly, according to the basic properties of chaotic systems, such as the sensitivity of the initial conditions and the one-to-one correspondence between chaotic orbit and the initial value, we established the nonlinear enlarge model based on the parabola map. Then, after we studied the nonlinear amplification of the parabola map, and the binary relationship between input and output, we achieved the simulation of the nonlinear amplification with common signals. Thirdly, we compared the result of linear amplification with nonlinear amplification; and discussed the advantages and disadvantages of nonlinear amplification under real situation. Finally, we get the conclusion that the weak signal amplification principle which is based on parabola map has superiority. It can reduce the noise while enlarging the useful signal. In other words, it can improve the signal to noise ratio.

Control and Applications of Chaos

1997 ◽  
Vol 07 (10) ◽  
pp. 2175-2197 ◽  
Author(s):  
Celso Grebogi ◽  
Ying–Cheng Lai ◽  
Scott Hayes
Keyword(s):  
Feedback Control ◽  
Power Systems ◽  
System Performance ◽  
Chaotic Systems ◽  
Electrical Power ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Chaotic Orbit ◽  
Electrical Power Systems ◽  
Dissipative Dynamical Systems

This review describes a procedure for stabilizing a desirable chaotic orbit embedded in a chaotic attractor of dissipative dynamical systems by using small feedback control. The key observation is that certain chaotic orbits may correspond to a desirable system performance. By carefully selecting such an orbit, and then applying small feedback control to stabilize a trajectory from a random initial condition around the target chaotic orbit, desirable system performance can be achieved. As applications, three examples are considered: (1) synchronization of chaotic systems; (2) conversion of transient chaos into sustained chaos; and (3) controlling symbolic dynamics for communication. The first and third problems are potentially relevant to communication in engineering, and the solution of the second problem can be applied to electrical power systems to avoid catastrophic events such as the voltage collapse.

Multiple Attractor Bifurcation in Three-Dimensional Piecewise Linear Maps

2018 ◽  
Vol 28 (10) ◽  
pp. 1830032 ◽  
Author(s):  
Mahashweta Patra
Keyword(s):  
Piecewise Linear ◽  
Three Dimensional ◽  
Chaotic Orbit ◽  
Stable And Unstable Manifolds ◽  
Period 2 ◽  
Coexistence Of Attractors ◽  
Linear Maps ◽  
Piecewise Linear Maps ◽  
Unstable Manifolds ◽  
Fundamental Uncertainty

Multiple attractor bifurcations lead to simultaneous creation of multiple stable orbits. This may be damaging for practical systems as there is a fundamental uncertainty regarding which orbit the system will follow after a bifurcation. Such bifurcations are known to occur in piecewise smooth maps, which model many practical and engineering systems. So far the occurrence of such bifurcations have been investigated in the context of 2D piecewise linear maps. In this paper, we investigate multiple attractor bifurcations in a three-dimensional piecewise linear normal form map. We show the occurrence of different types of multiple attractor bifurcations in the system, like the simultaneous creation of a period-2 orbit, a period-3 orbit and an unstable chaotic orbit; a mode-locked torus, an ergodic torus and periodic orbits; a one-loop torus and a two-loop torus; a one-loop mode-locked torus and a two-loop mode-locked torus; a one-piece chaotic orbit and a 3-piece chaotic orbit, etc. As orbits lie on unstable manifolds of fixed points, the structure of unstable manifold plays an important role in understanding the coexistence of attractors. In this work, we show that interplay between 1D and 2D stable and unstable manifolds plays an important role in global bifurcations that can give rise to multiple coexisting attractors.

Research on Chaotic Orbit in Mandelbrot Set

2014 ◽  
Vol 912-914 ◽  
pp. 1349-1352
Author(s):  
Tao Sui ◽  
Xiao Yu Zhang ◽  
Guang Shen Li ◽  
Guan Nan Liu
Keyword(s):  
Recurrence Formula ◽  
Periodic Points ◽  
Mandelbrot Set ◽  
Chaotic Orbit ◽  
Java Applet ◽  
Distribution Rules ◽  
Period Orbit ◽  
Fractal Images ◽  
Relationship Of ◽  
Stable Points

In this paper, the chaotic orbit in Mandelbrot set is introduced. On the basis of other scholars research, the character and distribution rules of pre-periodic orbits and pre-periodic points-Misiurewiz points about Mandelbrot set chaos-fractal images were studied. The software of constructing the general M-J set with Java Applet is improved. Using the method of computer mathematic experiments, the paper analyses the fixed orbit and period orbit in the M-set, gains the topology relationship of M set in super stable points, a recurrence formula between the period orbit and M-set periodic-buds is created.

On the Behaviour of Steamwhirl and Nonlinear Rotor-Bearing Systems

1993 ◽  
Author(s):  
Julio C. Gómez-Mancilla ◽  
Andrew D. Dimarogonas
Keyword(s):  
Limit Cycles ◽  
Tangential Force ◽  
Stable Limit ◽  
Slider Bearing ◽  
Chaotic Orbit ◽  
Element Analysis ◽  
Tilting Pad ◽  
Linearized System ◽  
Analytical Expressions ◽  
Stable Limit Cycles

Abstract The problem of steamwhirl is the technological limit which now prohibits the development of power generating turbomachinery substantially above 1 GW. Due to the steam flow, self excited vibrations develop at high loads, above the onset of instability of the linearized system, in the form of stable limit cycles which, at even higher loads, deteriorate to chaotic vibration. The bearing nonlinearity is introduced in the form of high order coefficients of a Taylor expansion of the perturbation forces for fixed-arc slider bearing and employing non-linear pad functions for the tilting pad bearings. The flow excitation is introduced in the form of radial and tangential force gradients related to the flow and power generated. The study of stable and unstable limit cycles and stability of the system in the large, beyond the linear analysis currently utilized, is done analytically for the DeLaval rotor and numerically with Finite Element analysis of typical turbomachinery rotors. The range of loads for which limit cycles exist was found to be substantial. This is important for the operation of large machinery because such limit cycles permit the operation at loads much higher than the ones which correspond to the onset of instability of the linearized system. The conditions for the limit cycle deterioration into chaotic orbit is studied. Analytical expressions have been obtained for the different thresholds for the DeLaval rotor.

scholarly journals An improved permutation-diffusion type image cipher with a chaotic orbit perturbing mechanism

2013 ◽  
Vol 21 (23) ◽  
pp. 27873 ◽  
Author(s):  
Jun-xin Chen ◽  
Zhi-liang Zhu ◽  
Chong Fu ◽  
Hai Yu
Keyword(s):  
Chaotic Orbit ◽  
Diffusion Type ◽  
Image Cipher
Sign in / Sign up

Export Citation Format

Share Document