DYNAMICS OF A PARTICULAR LORENZ TYPE SYSTEM

Giorgio E. Testoni () and Paulo C. Rech ()
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Giorgio E. Testoni: Departamento de Física, Universidade do Estado de Santa Catarina, 89223-100 Joinville, Brazil
Paulo C. Rech: Departamento de Física, Universidade do Estado de Santa Catarina, 89223-100 Joinville, Brazil

International Journal of Modern Physics C (IJMPC), 2010, vol. 21, issue 07, 973-982

Abstract: In this paper we analytically and numerically investigate the dynamics of a nonlinear three-dimensional autonomous first-order ordinary differential equation system, obtained from paradigmatic Lorenz system by suppressing theyvariable in the right-hand side of the second equation. The Routh–Hurwitz criterion is used to decide on the stability of the nontrivial equilibrium points of the system, as a function of the parameters. The dynamics of the system is numerically characterized by using diagrams that associate colors to largest Lyapunov exponent values in the parameter-space. Additionally, phase-space plots and bifurcation diagrams are used to characterize periodic and chaotic attractors.

Keywords: Phase-space; parameter-space; Lyapunov exponents; nonlinear differential equations; 02.30.Rz; 05.45.Pq; 05.45.Ac (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0129183110015580

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