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.

A CHAOTIC SYSTEM WITH ONE SADDLE AND TWO STABLE NODE-FOCI

2008 ◽  
Vol 18 (05) ◽  
pp. 1393-1414 ◽  
Author(s):  
QIGUI YANG ◽  
GUANRONG CHEN
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Autonomous System ◽  
Lorenz System ◽  
Complex Dynamics ◽  
Three Dimensional ◽  
Type Systems ◽  
Stable Node ◽  
Compound Structure ◽  
Chen System

This paper reports the finding of a chaotic system with one saddle and two stable node-foci in a simple three-dimensional (3D) autonomous system. The system connects the original Lorenz system and the original Chen system and represents a transition from one to the other. The algebraical form of the chaotic attractor is very similar to the Lorenz-type systems but they are different and, in fact, nonequivalent in topological structures. Of particular interest is the fact that the chaotic system has a chaotic attractor, one saddle and two stable node-foci. To further understand the complex dynamics of the system, some basic properties such as Lyapunov exponents, bifurcations, routes to chaos, periodic windows, possible chaotic and periodic-window parameter regions, and the compound structure of the system are analyzed and demonstrated with careful numerical simulations.

Research on Three Dimensional Design of Cavity of Injection Molds of Involute Plastic Gears

2012 ◽  
Vol 472-475 ◽  
pp. 2859-2863
Author(s):  
Guang Si Luo
Keyword(s):  
Injection Molding ◽  
Three Dimensional ◽  
Tooth Profile ◽  
Injection Molding Process ◽  
Molding Process ◽  
3D Design ◽  
Non Linear ◽  
Involute Gears ◽  
Plastic Gears ◽  
The Relationship

The crux to the 3D design of cavity of injection molds for involute plastic gears is to solve the difficulty in zooming the cavity of molds and the accurate molding of the involute tooth profile. Researches have shown that the shrinkage of involute tooth profile is non-linear during the injection molding process of plastic gears. This paper presents the 3D design of cavity of injection molds for involute gears based on SolidWorks after offering an introduction to the relationship between the cavity tooth profile of injection molds for small-modulus plastic gears and the tooth profile of injection molding part.

Buckling and Post-Buckling of Thin Elastoplastic Cylindrical Shells With Finite Rotations

2000 ◽  
Author(s):  
Philippe Le Grognec ◽  
Anh Le Van
Keyword(s):  
Yield Criterion ◽  
Kinematic Hardening ◽  
Three Dimensional ◽  
Thin Shells ◽  
Elastoplastic Material ◽  
Plane Stress Condition ◽  
Buckling Mode ◽  
Non Linear ◽  
Post Buckling ◽  
Non Linear System

Abstract An elastoplastic thin shell model is presented in this work in order to compute the buckling and post-buckling behavior of cylindrical shell-type structures. Standard assumptions in the shell kinematics allow us to develop a large deformation and finite rotation model for thin shells from the three-dimensional continuum. An elastoplastic constitutive model for thin shells is derived from the three-dimensional framework, assuming the plane stress condition. The von Mises yield criterion is adopted including non-linear isotropic and linear kinematic hardening. The resulting non-linear system is solved by a Newton-Raphson solution procedure, including the consistent linearization of the shell kinematics and the elastoplastic material model. The high non-linearities due to the buckling-type instabilities, especially those occuring in the neighbourhood of critical points, necessitate the use of an appropriate step-length control. An arc-length method has been successfully implemented for passing through limit points (load or displacement peaks) where pure load or displacement controls fail. The proposed method is effective in handling both sharp snap-throughs and snap-backs. Two numerical examples are presented in view of the assessment of the proposed approach and a particular attention is devoted to the post-buckling of hollow cylinders under axial compression. We identify several types of buckling mode for these structures, among which the axisymmetric mode, the “diamond” mode and the “elephant foot” mode, depending on geometry and boundary conditions.

Analysis of Maximum Expiratory Flow Volume Curves Using Canonical Correlation Analysis

1985 ◽  
Vol 24 (02) ◽  
pp. 91-100 ◽  
Author(s):  
W. van Pelt ◽  
Ph. H. Quanjer ◽  
M. E. Wise ◽  
E. van der Burg ◽  
R. van der Lende
Keyword(s):  
Correlation Analysis ◽  
Canonical Correlation Analysis ◽  
Canonical Correlation ◽  
Flow Volume ◽  
Non Linear ◽  
Maximum Expiratory Flow ◽  
Expiratory Flow ◽  
Relationship Of ◽  
The Relationship ◽  
Age And Sex

SummaryAs part of a population study on chronic lung disease in the Netherlands, an investigation is made of the relationship of both age and sex with indices describing the maximum expiratory flow-volume (MEFV) curve. To determine the relationship, non-linear canonical correlation was used as realized in the computer program CANALS, a combination of ordinary canonical correlation analysis (CCA) and non-linear transformations of the variables. This method enhances the generality of the relationship to be found and has the advantage of showing the relative importance of categories or ranges within a variable with respect to that relationship. The above is exemplified by describing the relationship of age and sex with variables concerning respiratory symptoms and smoking habits. The analysis of age and sex with MEFV curve indices shows that non-linear canonical correlation analysis is an efficient tool in analysing size and shape of the MEFV curve and can be used to derive parameters concerning the whole curve.

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