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Symmetry breaking and bifurcations in complex Lorenz model. (Ukrainian. English summary) Zbl 1079.37504

Summary: The concept of broken symmetry is used to study stability of equilibrium and time doubly-periodic bifurcating solutions of the complex nonresonant Lorenz model as a function of the frequency detuning on the basis of modified Hopf theory. By contrast to the well-known real Lorenz equations, the system in question is invariant under the action of Lie group transformations (rotations in complex planes) and an invariant set of stationary points is found to bifurcate into an invariant torus, which is stable under the detuning exceeding its critical value. If the detuning then goes downward, numerical analysis reveals that after a cascade of period-doublings the strange Lorenz attractor is formed in the vicinity of zero detuning.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C60 Qualitative investigation and simulation of ordinary differential equation models
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
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