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Velocity-dependent Lyapunov exponents as a measure of chaos for open-flow systems
Institution:1. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigradsko Chaussee, Blvd., 1784 Sofia, Bulgaria;2. Department of Applied Mathematics and Computer Science, Technical University of Sofia, 8 Kliment Ohridski, Blvd., 1000 Sofia, Bulgaria;1. Department of Chemistry, University of Kalyani, Kalyani, Nadia 741235, WB, India;2. Department of Physics, Acharya Prafulla Chandra College, New Barrackpore, Kolkata 700131, India;3. Immunology Laboratory, Department of Zoology, University of Calcutta, 35 Ballygunge Circular Road, Kolkata 700019, India;4. Department of Chemistry, Missouri University of S & T, Rolla, MO 65409, USA;1. Laboratory of Electronics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon;2. Department of Physics, Higher Teacher Training College Yaounde, University of Yaounde I, P.O. Box 47, Yaounde, Cameroon;3. Department of Physics, Faculty of Science, Moulay Ismail University, P.O. Box. 1120, Meknes, Morocco;4. Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon;5. Centre d׳Excellence Africain des Technologies de l׳Information et de la Communication (CETIC), Université de Yaoundé I, Cameroon
Abstract:Many flows in nature are “open flows” (e.g. pipe flow). We study two open-flow systems driven by low-level external noise: the time-dependent generalized Ginzburg-Landau equation and a system of coupled logistic maps. We find that a flow which gives every appearance of being chaotic may nonetheless have no positive Lyapunov exponents. By generalizing the notions of convective instability and Lyapunov exponents we define a measure of chaos for these flows.
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