Novel Hyperchaotic System and Its Circuit Implementation

2015 ◽  
Vol 10 (6) ◽  
Author(s):  
Chaowen Feng ◽  
Li Cai ◽  
Qiang Kang ◽  
Sen Wang ◽  
Hongmei Zhang
Keyword(s):  
Circuit Design ◽  
Piecewise Linear ◽  
Linear Functions ◽  
Theoretical Research ◽  
Secure Communications ◽  
Hyperchaotic System ◽  
State Equations ◽  
Random Nature ◽  
Theoretical Analyses ◽  
New Hyperchaotic System

It is very important to generate hyperchaos with more complicated dynamics as a model for theoretical research and practical application. A new hyperchaotic system with double piecewise-linear functions in state equations is presented and physically implemented by circuit design. Based on the theoretical analyses and simulations, the hyperchaotic dynamical properties of this nonlinear system are revealed by equilibria, Lyapunov exponents, and bifurcations, verifying its unusual random nature and indicating its great potential for some relevant engineering applications such as secure communications.

GENERATION AND IMPLEMENTATION OF HYPERCHAOTIC CHUA SYSTEM VIA STATE FEEDBACK CONTROL

2012 ◽  
Vol 22 (05) ◽  
pp. 1250119 ◽  
Author(s):  
HUILING XI ◽  
SIMIN YU ◽  
CHAOXIA ZHANG ◽  
YOULIN SUN
Keyword(s):  
Feedback Control ◽  
Theoretical Analysis ◽  
State Feedback ◽  
Piecewise Linear ◽  
State Feedback Control ◽  
Hyperchaotic System ◽  
Cubic Nonlinearity ◽  
State Equations ◽  
Dynamical Behaviors ◽  
Simulation Based

In this paper, a 4D hyperchaotic Chua system both with piecewise-linear nonlinearity and with smooth and piecewise smooth cubic nonlinearity is introduced, based on state feedback control. Dynamical behaviors of this hyperchaotic system are further investigated, including Lyapunov exponents spectrum, bifurcation diagram and solution of state equations. Theoretical analysis and numerical results show that this system can generate multiscroll hyperchaotic attractors. In addition, a circuit is designed for 4D hyperchaotic Chua system such that the double-scroll and 3-scroll hyperchaotic attractors can be physically obtained, demonstrating the effectiveness of the proposed simulation-based techniques.

A HYPERCHAOTIC CHUA SYSTEM

2009 ◽  
Vol 19 (11) ◽  
pp. 3823-3828 ◽  
Author(s):  
PAULO C. RECH ◽  
HOLOKX A. ALBUQUERQUE
Keyword(s):  
Linear Function ◽  
Piecewise Linear ◽  
Dynamical Behavior ◽  
Piecewise Linear Function ◽  
Hyperchaotic System ◽  
Cubic Polynomial ◽  
New Hyperchaotic System

In this paper, we report a new four-dimensional autonomous hyperchaotic system, constructed from a Chua system where the piecewise-linear function usually taken to describe the nonlinearity of the Chua diode has been replaced by a cubic polynomial. Analytical and numerical procedures are conducted to study the dynamical behavior of the proposed new hyperchaotic system.

On a new hyperchaotic system

2008 ◽  
Vol 372 (2) ◽  
pp. 124-136 ◽  
Author(s):  
Guoyuan Qi ◽  
Michaël Antonie van Wyk ◽  
Barend Jacobus van Wyk ◽  
Guanrong Chen
Keyword(s):  
Hyperchaotic System ◽  
New Hyperchaotic System

Modelling the single-electron transistor with piecewise linear functions

2009 ◽  
Author(s):  
Arturo Sarmiento-Reyes ◽  
Luis Hernandez-Martinez ◽  
Miguel Angel Gutierrez de Anda ◽  
Francisco Javier Castro Gonzalez
Keyword(s):  
Piecewise Linear ◽  
Linear Functions ◽  
Single Electron ◽  
Single Electron Transistor ◽  
Piecewise Linear Functions

Mesh duality and Legendre duality

1990 ◽  
Vol 428 (1875) ◽  
pp. 351-377 ◽  
Keyword(s):  
Piecewise Linear ◽  
Voronoi Tessellation ◽  
Tangent Plane ◽  
Linear Functions ◽  
Piecewise Linear Functions ◽  
Dual Transformation ◽  
Delaunay Mesh ◽  
Definition Of

We describe a sense in which mesh duality is equivalent to Legendre duality. That is, a general pair of meshes, which satisfy a definition of duality for meshes, are shown to be the projection of a pair of piecewise linear functions that are dual to each other in the sense of a Legendre dual transformation. In applications the latter functions can be a tangent plane approximation to a smoother function, and a chordal plane approximation to its Legendre dual. Convex examples include one from meteorology, and also the relation between the Delaunay mesh and the Voronoi tessellation. The latter are shown to be the projections of tangent plane and chordal approximations to the same paraboloid.

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