The non-piecewise-linear autonomous system. I. More details on the periodic waveforms

2002 ◽  
Author(s):  
Yu Zhiping ◽  
Zhao Jing
Keyword(s):  
Autonomous System ◽  
Piecewise Linear ◽  
Linear Autonomous System

GENERATING 3-D SCROLL GRID ATTRACTORS OF FRACTIONAL DIFFERENTIAL SYSTEMS VIA STAIR FUNCTION

2007 ◽  
Vol 17 (11) ◽  
pp. 3965-3983 ◽  
Author(s):  
WEIHUA DENG
Keyword(s):  
Differential System ◽  
Autonomous System ◽  
Function Approach ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential System ◽  
Linear Autonomous System ◽  
Fractional Differential ◽  
The One ◽  
Number Of Equilibria

This paper discusses the stair function approach for the generation of scroll grid attractors of fractional differential systems. The one-directional (1-D) n-grid scroll, two-directional (2-D) (n × m)-grid scroll and three-directional (3-D) (n × m × l)-grid scroll attractors are created from a fractional linear autonomous system with a simple stair function controller. Being similar to the scroll grid attractors of classical differential systems, the scrolls of 1-D n-grid scroll, 2-D (n × m)-grid scroll and 3-D (n × m × l)-grid scroll attractors are located around the equilibria of fractional differential system on a line, on a plane or in 3D, respectively and the number of scrolls is equal to the corresponding number of equilibria.

GENERATING CHAOS VIA A DYNAMICAL CONTROLLER

2001 ◽  
Vol 11 (03) ◽  
pp. 865-869 ◽  
Author(s):  
GUO-QUN ZHONG ◽  
KIM F. MAN ◽  
GUANRONG CHEN
Keyword(s):  
Computer Simulation ◽  
Autonomous System ◽  
Quadratic Function ◽  
Feedback Controller ◽  
Nonlinear Feedback ◽  
Circuit Implementation ◽  
Linear Autonomous System

This Letter studies the generation of chaos from a linear autonomous system by employing a dynamical nonlinear feedback controller. The system setup is quite simple, and the only nonlinearity is a piecewise-quadratic function in the form of x|x|. Both computer simulation and circuit implementation are given to verify the chaos generated by this mechanism.

scholarly journals A Chaotic Three Dimensional Non-Linear Autonomous System Beyond Lorenz Type Systems

2012 ◽  
Vol 36 (2) ◽  
pp. 159-170
Author(s):  
Md Shariful Islam Khan ◽  
Md Shahidul Islam
Keyword(s):  
Autonomous System ◽  
Three Dimensional ◽  
Type Systems ◽  
Control Parameters ◽  
Fundamental Properties ◽  
Non Linear ◽  
Linear Autonomous System ◽  
Non Linear System ◽  
Academy Of Sciences ◽  
The Relationship

Some fundamental properties of a chaotic three-dimensional non-linear system of the Lorenz type systems were studied. The invariance, dissipation, bifurcation and the strange attractors were investigated and analyzed one 1-scroll, two 2-scroll and two 4-scroll attractors by adding control   parameters to this system. The relationship and connecting function for the 2-scroll attractor of this system were also explored. DOI: http://dx.doi.org/10.3329/jbas.v36i2.12959 Journal of Bangladesh Academy of Sciences, Vol. 36, No. 2, 159-170, 2012  

Existence and stability of periodic solutions of a third-order non-linear autonomous system simulating immune response in animals

1977 ◽  
Vol 77 (1-2) ◽  
pp. 163-175 ◽  
Author(s):  
In-Ding Hsü ◽  
Nicholas D. Kazarinoff
Keyword(s):  
Immune Response ◽  
Steady State ◽  
Periodic Solutions ◽  
Stability Criterion ◽  
Autonomous System ◽  
Third Order ◽  
Non Linear ◽  
Existence And Stability ◽  
Linear Autonomous System ◽  
Non Linear System

SynopsisA 3 × 3 autonomous, non-linear system of ordinary differential equations modelling the immune response in animals to invasion by active self-replicating antigens has been introduced by G. I. Bell and studied by G. H. Pimbley Jr. Using Hopf's theorem on bifurcating periodic solutions and a stability criterion of Hsu and Kazarinoff, we obtain existence of a family of unstable periodic solutions bifurcating from one steady state of a reduced 2×2 form of the 3×3 system. We show that no periodic solutions bifurcate from the other steady state. We also prove existence and exhibit a stability criterion for families of periodic solutions of the full 3×3 system. We provide two numerical examples. The second shows existence of orbitally stable families of periodic solutions of the 3×3 system.

Sign in / Sign up

Export Citation Format

Share Document