An application of the theory of monotone systems to an electrical circuit

2002 ◽  
Vol 132 (3) ◽  
pp. 711-728 ◽  
Author(s):  
Luis A. Sánchez
Keyword(s):  
Systems Theory ◽  
Autonomous System ◽  
Three Dimensional ◽  
Electrical Circuit ◽  
Monotone Systems ◽  
Periodic Oscillations ◽  
Stable Periodic ◽  
Nonlinear Autonomous System

This paper considers the dynamics of a three-dimensional nonlinear autonomous system that models the behaviour of an electrical circuit. Results on the existence of stable periodic oscillations and the behaviour of Poincaré–Bendixon types are obtained. The work is based on a variation of classical monotone systems theory.

Asymptotic Behaviour and Hopf Bifurcation of a Three-Dimensional Nonlinear Autonomous System

2002 ◽  
Vol 9 (2) ◽  
pp. 207-226
Author(s):  
Lenka Baráková
Keyword(s):  
Hopf Bifurcation ◽  
Autonomous System ◽  
Three Dimensional ◽  
Invariant Set ◽  
Concrete Type ◽  
Cubic System ◽  
Dynamic Version ◽  
Globally Attractive ◽  
Nonlinear Autonomous System ◽  
Positively Invariant Set

Abstract A three-dimensional real nonlinear autonomous system of a concrete type is studied. The Hopf bifurcation is analyzed and the existence of a limit cycle is proved. A positively invariant set, which is globally attractive, is found using a suitable Lyapunov-like function. Corollaries for a cubic system are presented. Also, a two-dimensional nonlinear system is studied as a restricted system. An application in economics to the Kodera's model of inflation is presented. In some sense, the model of inflation is an extension of the dynamic version of the neo-keynesian macroeconomic IS-LM model and the presented results correspond to the results for the IS-LM model.

Digitalization of production in Altium Designer software

2021 ◽  
pp. 34-42
Author(s):  
S. S. Yudachev ◽  
S. S. Sitnikov ◽  
F. M. Bosy
Keyword(s):  
Printed Circuit Boards ◽  
Electronic Device ◽  
Educational Institution ◽  
Three Dimensional ◽  
Electrical Circuit ◽  
Circuit Board ◽  
Practical Significance ◽  
Three Dimensional Model ◽  
Printed Circuit ◽  
Higher Educational

A method for modeling and printed circuit board layout in the form of a 3D model in one of the digital solutions designed for this task, Altium Designer, is proposed. The practical significance of the work is the study of the basic software libraries in terms of their creation, filling and application when working with the project, as well as of the algorithm for constructing an electrical circuit in the Altium Designer program, layout and design of the simplest circuit on the board. In the course of the work, the algorithm and rules for creating a library of three-dimensional models of components, a library containing conditional graphic designations of the corresponding components, a schematic diagram of the device, a three-dimensional model of the board and the construction of conducting tracks on it are described. The components and circuits used in the work are publicly available on the Internet, which allows anyone to work over the entire algorithm for studying and honing the skills of designing printed circuit boards, both by students studying at a higher educational institution and by fully-fledged specialists. This work can be used not only for teaching students in the field of electronic device development in terms of their design and for organizing laboratory work, but also for creating and designing real devices both in production and within a higher educational institution, for example, for creating a laboratory bench. The introduction and study of this software is carried out at the Department of Radio-Electronic Systems and Complexes of one of the leading engineering universities of the Russian Federation — the Bauman Moscow State Technical University.

The analysis of complex behaviours of a novel three dimensional autonomous system

2010 ◽  
Vol 19 (7) ◽  
pp. 070514
Author(s):  
Dong Gao-Gao ◽  
Zheng Song ◽  
Tian Li-Xin ◽  
Du Rui-Jin ◽  
Sun Mei
Keyword(s):  
Autonomous System ◽  
Three Dimensional

scholarly journals Discontinuous Spirals of Stable Periodic Oscillations

2013 ◽  
Vol 3 (1) ◽  
Author(s):  
Achim Sack ◽  
Joana G. Freire ◽  
Erik Lindberg ◽  
Thorsten Pöschel ◽  
Jason A. C. Gallas
Keyword(s):  
Periodic Oscillations ◽  
Stable Periodic

scholarly journals Periodic orbits relevant for the formation of inner rings in barred galaxies

1985 ◽  
Vol 106 ◽  
pp. 543-544
Author(s):  
M. Michalodimitrakis ◽  
Ch. Terzides
Keyword(s):  
Periodic Orbits ◽  
Three Dimensional ◽  
Particle Trapping ◽  
Barred Galaxies ◽  
Future Paper ◽  
Stability Of Periodic Orbits ◽  
Wide Range ◽  
The Galaxy ◽  
Stable Periodic ◽  
The Stability

The study of orbits of a test particle in the gravitational field of a model barred galaxy is a first step toward the understanding of the origin of the morphological characterstics observed in real barred galaxies. In this paper we confine our attention to the inner rings. Inner rings are a very common characteristic of barred galaxies. They are narrow, round or slightly elongated along the bar (with typical axial ratios from 0.7 to near 1.0), and of the same size as the bar. A first step to test the old hypothesis that inner rings consist of stars trapped near stable periodic orbits would be a study of particle trapping around periodic orbits encircling the bar. Such a study is contained in the work of several authors (Danby 1965, de Vaucouleurs and Freeman 1972, Michalodimitrakis 1975, Contopoulos and Papayannopoulos 1980, Athanassoula et al. 1983). In the above works the stability of periodic orbits was studied with respect to perturbations which lie on the plane of motion z = 0 (planar stability). To ensure the possibility of formation of rings, a study of stability with respect to perturbations perpendicular to the plane of motion (vertical stability) is necessary. In this paper we investigate the properties of periodic orbits which we believe to be relevant for the inner-ring problem using a sufficiently general model for the galaxy and sets of values for the parameters which cover a wide range of different possible cases. We also study the stability, planar and vertical, with respect to large perturbations in order to estimate the extent of particle trapping. A detailed numerical investigation of three-dimensional periodic orbits will be given in a future paper.

A 3D Autonomous System with Infinitely Many Chaotic Attractors

2019 ◽  
Vol 29 (12) ◽  
pp. 1950166 ◽  
Author(s):  
Ting Yang ◽  
Qigui Yang
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Autonomous System ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Double Zero ◽  
Finite Dimensional ◽  
Periodic Attractors ◽  
The Stability ◽  
Autonomous Dynamical System

Intuitively, a finite-dimensional autonomous system of ordinary differential equations can only generate finitely many chaotic attractors. Amazingly, however, this paper finds a three-dimensional autonomous dynamical system that can generate infinitely many chaotic attractors. Specifically, this system can generate infinitely many coexisting chaotic attractors and infinitely many coexisting periodic attractors in the following three cases: (i) no equilibria, (ii) only infinitely many nonhyperbolic double-zero equilibria, and (iii) both infinitely many hyperbolic saddles and nonhyperbolic pure-imaginary equilibria. By analyzing the stability of double-zero and pure-imaginary equilibria, it is shown that the classic Shil’nikov criteria fail in verifying the existence of chaos in the above three cases.

scholarly journals Hopf Bifurcation, Positively Invariant Set, and Physical Realization of a New Four-Dimensional Hyperchaotic Financial System

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
G. Kai ◽  
W. Zhang ◽  
Z. C. Wei ◽  
J. F. Wang ◽  
A. Akgul
Keyword(s):  
Hopf Bifurcation ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Financial System ◽  
Invariant Set ◽  
Phase Portraits ◽  
Lyapunov Coefficient ◽  
Stable Periodic ◽  
Analytical Proof ◽  
Positively Invariant Set

This paper introduces a new four-dimensional hyperchaotic financial system on the basis of an established three-dimensional nonlinear financial system and a dynamic model by adding a controller term to consider the effect of control on the system. In terms of the proposed financial system, the sufficient conditions for nonexistence of chaotic and hyperchaotic behaviors are derived theoretically. Then, the solutions of equilibria are obtained. For each equilibrium, its stability and existence of Hopf bifurcation are validated. Based on corresponding first Lyapunov coefficient of each equilibrium, the analytical proof of the existence of periodic solutions is given. The ultimate bound and positively invariant set for the financial system are obtained and estimated. There exists a stable periodic solution obtained near the unstable equilibrium point. Finally, the dynamic behaviors of the new system are explored from theoretical analysis by using the bifurcation diagrams and phase portraits. Moreover, the hyperchaotic financial system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integrations and its real contribution to engineering.

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