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The work is devoted to the study of the features of the Earth’s magnetosphere dynamics. It is shown that in each of the 11-year cycles of solar activity the dynamics of the magnetosphere activity (Ap and AL-indices) demonstrates a sharp transition (trigger mode) from the “periodic” regime (low level of broadband noise, the presence of a 27-day periodicity) to a “chaotic” (high level of broadband noise, lack of a 27-day periodicity). The goal of this work is to search of the parameter of the solar activity dynamics and/or the interplanetary medium which determines the switching of the magnetosphere regimes. We used for the analysis series of daily values of the solar activity and interplanetary medium parameters during the period of 1932 - 2016. It has been found that the dynamics of the spectral characteristics and the trigger properties of the Ap and AL indices correlate with the dynamics of the solar wind parameter β (β is ratio of the plasma pressure to magnetic pressure). It is shown that the change of the magnetosphere regime “chaos - periodicity” is determined by the β value. The “chaotic” and “periodic” regimes in the dynamics of the magnetosphere are observed at β≤1 and at β>1 respectively. We note that the level of turbulent fluctuations in the solar wind reaches its maximum values precisely at β ~ 1 [1]. Consequently, the ratio of the plasma pressure to magnetic pressure is the parameter that determines the switching regime in the magnetosphere dynamics. The change of the β in the 11-year cycle of solar activity is determined by the dynamics of the inclination angle of the magnetic dipole axis of the Sun [2, 3]. Thus, the global geoeffective parameter determining the particular features of the dynamics of the magnetosphere activity is the inclination angle of the magnetic dipole axis of the Sun to the ecliptic plane. This work was supported by Russian Foundation for Basic Research 16-05-00056, Government task 0144-2014-00116. REFERENCES 1. Chernyshov A.A., Karelsky K.V., Petrosyan A.S. Subgrid-scale modeling for the study of compressible magnetohydrodynamic turbulence in space plasmas // UFN. 2014. V. 184 (5). P. 457 - 492. 2. Livshits I.M. Obridko V.N. Variations of the dipole magnetic moment of the sun during the solar activity cycle // Astron. Rep. 2006. V. 50: 926. doi:10.1134/S1063772906110060. 3. Sokolov I. V., Bart van der Holst, Rona Oran et al. Magnetohydrodynamic waves and coronal heating: unifying empirical and MHD turbulence models // The Astrophysical Journal. 2013. V.764: 23. 13pp. doi:10.1088/0004-637X/764/1/23.