NUMERICAL INTEGRATION AND STABILITY PROBLEMS IN THE STUDY OF LORENZ SYSTEM

Camelia POP ARIESANU

Abstract


The differential equations systems with chaotic behavior have been studied in the last twenty years due to their deep applications in many engineering-oriented applied fields, such as nonlinear circuits, synchronization, lasers or secure communications. The first canonical chaotic attractor was found by Lorenz in 1963 when he studied the atmospheric convection phenomenon in three-dimensional. The goal of our paper is to study this system from the mechanical geometry point of view: nonlinear stability problems via energy-Casimir method, periodical orbits, numerical integration via Poisson integrator and numerical simulation.

Key words: Lorenz system, Hamilton-Poisson realization, nonlinear stability, Lie-Trotter integrator, Kahan  integrator.

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