Exact Analytical Periodic Solutions in Special Cases and Numerical Analysis of a Half-Undamped 1-DOF Piecewise-Linear Vibratory System

2021 ◽  
pp. 783-792
Author(s):  
Minh-Tuan Nguyen-Thai
Keyword(s):  
Numerical Analysis ◽  
Periodic Solutions ◽  
Piecewise Linear ◽  
Vibratory System ◽  
Special Cases

HYPERCHAOS IN A MODIFIED CANONICAL CHUA'S CIRCUIT

2004 ◽  
Vol 14 (01) ◽  
pp. 221-243 ◽  
Author(s):  
K. THAMILMARAN ◽  
M. LAKSHMANAN ◽  
A. VENKATESAN
Keyword(s):  
Numerical Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Laboratory Experiments ◽  
System Parameter ◽  
Piecewise Linear ◽  
Electrical Circuit ◽  
First Order ◽  
Regular Behavior ◽  
Linear Elements

In this paper, we present the hyperchaos dynamics of a modified canonical Chua's electrical circuit. This circuit, which is capable of realizing the behavior of every member of the Chua's family, consists of just five linear elements (resistors, inductors and capacitors), a negative conductor and a piecewise linear resistor. The route followed is a transition from regular behavior to chaos and then to hyperchaos through border-collision bifurcation, as the system parameter is varied. The hyperchaos dynamics, characterized by two positive Lyapunov exponents, is described by a set of four coupled first-order ordinary differential equations. This has been investigated extensively using laboratory experiments, Pspice simulation and numerical analysis.

scholarly journals Limit Cycles Bifurcating from the Periodic Orbits of a Discontinuous Piecewise Linear Differentiable Center with Two Zones

2015 ◽  
Vol 25 (11) ◽  
pp. 1550144 ◽  
Author(s):  
Jaume Llibre ◽  
Douglas D. Novaes ◽  
Marco A. Teixeira
Keyword(s):  
Equilibrium Point ◽  
Periodic Solutions ◽  
Periodic Orbits ◽  
Limit Cycles ◽  
Homoclinic Orbit ◽  
Piecewise Linear ◽  
Differential Systems ◽  
Linear Differential Systems ◽  
Straight Line ◽  
Linear Differential

We study a class of discontinuous piecewise linear differential systems with two zones separated by the straight line x = 0. In x > 0, we have a linear saddle with its equilibrium point living in x > 0, and in x < 0 we have a linear differential center. Let p be the equilibrium point of this linear center, when p lives in x < 0, we say that it is real, and when p lives in x > 0 we say that it is virtual. We assume that this discontinuous piecewise linear differential system formed by the center and the saddle has a center q surrounded by periodic orbits ending in a homoclinic orbit of the saddle, independent if p is real, virtual or p is in x = 0. Note that q = p if p is real or p is in x = 0. We perturb these three classes of systems, according to the position of p, inside the class of all discontinuous piecewise linear differential systems with two zones separated by x = 0. Let N be the maximum number of limit cycles which can bifurcate from the periodic solutions of the center q with these perturbations. Our main results show that N = 2 when p is on x = 0, and N ≥ 2 when p is a real or virtual center. Furthermore, when p is a real center we found an example satisfying N ≥ 3.

scholarly journals Analysis of Special Cases in the Study of Bifurcations of Periodic Solutions of the Ikeda Equation

2020 ◽  
Vol 16 (3) ◽  
pp. 437-451
Author(s):  
E.P. Kubyshkin ◽  
◽  
A.R. Moriakova ◽  
Keyword(s):  
Periodic Solutions ◽  
Special Cases

A two-step iterative method based on diagonal and off-diagonal splitting for solving linear systems

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1441-1452
Author(s):  
Mehdi Dehghana ◽  
Marzieh Dehghani-Madisehb ◽  
Masoud Hajarianc
Keyword(s):  
Numerical Analysis ◽  
Linear Systems ◽  
Iterative Methods ◽  
Classical Problem ◽  
Coefficient Matrix ◽  
New Method ◽  
Step Method ◽  
Numerical Examples ◽  
Special Cases ◽  
Two Parameter

Solving linear systems is a classical problem of engineering and numerical analysis which has various applications in many sciences and engineering. In this paper, we study efficient iterative methods, based on the diagonal and off-diagonal splitting of the coefficient matrix A for solving linear system Ax = b, where A ? Cnxn is nonsingular and x,b ? Cnxm. The new method is a two-parameter two-step method that has some iterative methods as its special cases. Numerical examples are presented to illustrate the effectiveness of the new method.

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