Analysis of the Phaseportrait for the Lü Dynamical System in a Particular Case
Journal Title: ANALELE UNIVERSITATII DIN CRAIOVA - Seria Inginerie electrica - Year 2018, Vol 42, Issue 0
Abstract
In the present paper it is started a qualitative analysis of the Lü dynamical system, using the appropiate tools of Hamilton-Poisson geometry and using the software for mathematics MAPLE 15. The Lü’s system arise from electrical engineering networks and it is very known that he has a chaotic behavior. For this reason, the problem of finding the solution of the system could be very difficult. By obtaining of a geometric Hamilton-Poisson structure, we can find such a solution as the intersection of two surfaces, the surfaces equation being given by the Hamiltonian and the Casimir function . Using MAPLE 15, it will be analyzed the phase portrait for two particular simplified versions of the dynamical system associated to the Lü ordinary differential system (a=0, b=c=0 and a=1, b=c=0). Also, we will do a study of the Lyapunov stability of Lü’s system for the particular case (a=1, b=c=0). We obtain that the origin is an unstable equilibrium point for this particular parameter case of the Lü’s model. This fact is confirmed by the numerical simulations. More that, the pictures show that the origin is a non-stable focus, in the first simulation case. Analytical results are accompanied by numerical illustrations.
Authors and Affiliations
Adela Ionescu, Florian Munteanu
Keywords
Related Articles
- EP ID EP433248
- DOI -
- Views 99
- Downloads 0
Hardware Experiments for Simultaneous Control of Several Motors by a Microcontroller and a VHL Programming Language
The paper presents a hardware solution for the digital control of a multi-motor drive system using a very high level programming language and a single microcontroller. It follows a previous one for developing the softwar...
CPC−Founded Clarification of Decline of the Effectiveness of the Energy Transfer in Power Systems
The paper is focused on physical phenomena that degrade the effectiveness of the energy transfer in electrical systems when voltages and currents are nonsinusoidal and asymmetrical. The Currents’ Physical Components (CPC...
COMPUTATIONAL ANALYSIS OF HYDRODYNAMIC EFFECTS IN HYDRAULIC FLOW TURBINES (PART 1)
Research and elaboration of the systems for conversion of renewable energy sources (RSE) as a research objective present great interest and importance. Hydraulic energy currently is one of the most used, cheap and clean...
A "SMARTGRIDS-ASSISTANT" FOR POWER GRID OPERATION AND TRAINING
SmartGrids are understood as cell-wise structured, intelligent supply areas with own, distributed and renewable generators and storages. The actual intelligence is the IT-supported structure and control, especially to ma...
DEVELOPMENT, MANUFACTURE AND TESTING OF HORIZONTAL AXIS WIND MICROTURBINES WITH POWER OF 10 KW
Under the circumstances of the total energetic recourses deficit in the Republic of Moldova appears the problem of non-traditional sources utilization recovered by energy. Important sources of renewable energy are the wi...