
N.A. Magnitskii Running waves and spatiotemporal chaos in the generalized KuramotoSivashinsky equation 

Abstract. The analytical and numerical analysis of the transition to spatiotemporal chaos in the generalized KuramotoSivashinsky equation through cascades of traveling wave bifurcations is performed in accordance with the universal FeigenbaumSharkovskyMagnitskii bifurcation scenario. It is proved that the bifurcation parameter is the magnitude of the propagation velocity of traveling waves along the spatial axis, which is clearly not included in the initial equation. Keywords: generalized KuramotoSivashinsky equation, FSMcascade of bifurcations, traveling waves, singular attractors. PP. 96100. DOI: 10.14357/20790279180409 References 1. Magnitskii N.A. Begushchiye volny i prostranstvennovremennoy khaos v uravnenii KuramotoSivashinskogo [Running waves and spatiotemporal chaos in the KuramotoSivashinsky equation] // Differentsial’nyye uravneniya [Differential Equations]. 2018. v.54, No.9, p.1292–1296 2. Kudryashov N.A. Metody nelineynoy matematicheskoy fiziki [Methods of nonlinear mathematical physics]. M.: MIFI, 2008. 352 s. 3. Magnitskii N.A., Sidorov S.V. New methods for chaotic dynamics (monograph). Singapore: World Scientific, 2006. 363 p. 4. Magnitskii N.A. Teoriya dinamicheskogo khaosa [Theory of dynamical chaos]. M.: Lenand, 2011. 320s. 5. Magnitskii N.A. Universality of Transition to Chaos in All Kinds of Nonlinear Differential Equations. Chapter in Nonlinearity, Bifurcation and Chaos – Theory and Applications. INTECH, 2012. P.133174. 6. Evstigneev N.M., Magnitskii N.A. Numerical analysis of laminarturbulent bifurcation scenarios in KelvinHelmholtz and RayleighTaylor instabilities for compressible flow. Chapter in Turbulence. INTECH,2017.P.2959. 7. Magnitskii N.A. Bifurcation Theory of Dynamical Chaos. Chapter in Chaos Theory. INTECH, 2018, P. 197215.
