
PresentationsResearch Of Dynamical Systems Based on padic AnalysisFSBEU HPE MSTU (STANKIN), Russia, 127055, Moscow, Vadkovsky Lane, 3A, +79999047908, Email: phyowailinnmipt@gmail.com +74999729459, Email: uvar11@yandex.ru At present time, research in the field of chaotic systems is great interest. In particular, this is due to the need to find chaotic attractors, many of which have practical applications [1]. At the same time, it seems relevant to use padic analysis to study nonlinear dynamical systems. As showed result, which obtained in [2–4], this approach is presented as quite effective. In the present work, this approach is used to simulate the processes of phase transitions of the “liquidgas” type. Molecular structures of phases are modeled by a node – communication system. In particular, it can be a Cayley tree with a root at the phase boundary. To analyze the padic model, use the Hamiltonian model: $H=H_{v}+H_{g}$ (1) $H_{v} \left ( \sigma \right ) =J_{v} \sum _{(x,y)\in L_{v}}\delta _{\sigma (x_{v})\sigma (y_{v}),} H_{g}(\sigma )=J_{g} \sum _{(x,y)\in L_{g}}\delta _{\sigma (x_{g})\sigma (y_{g})},$ (2) Index $v$ refers to the liquid phase, index $g$ refers to the gas phase, $J_{v}$ $J_{g}$ are the coupling constants, $\delta _{ij}$  the Kronecker delta, $L_{v},L_{g}$ characterize the geometry of the sets. It is shown that the Gibbs energy can change abruptly from a limited value to infinity, which indicates the possibility of a phase transition and, accordingly, the breaking of bonds. This work is supported by the Russian Scientific Foundation (grant No. 181100247). References 1. Shao Fu Wang, DaZhuan Xu. The dynamic analysis of a chaotic system .– Beijing, China: Advances in Mechanical Engineering, 2017. Vol. 9(3) 1–6. 2. Wang Z, Zhou L, Chan Z. Local bifurcation analysis and topological horseshoe 4D of a hyperchaotic system. Nonlinear Dynamics 2016; 83: 20552066. 3. Farrukh Mukhamedov, Otabek Khakimov. Phase transition and chaos: P adic Potts model on a Cayley tree. – Madrid, Italy: Chaos, Solitons and Fractals 87 (2016) 190–196. 4. Rozikov UA , Khakimov R . Periodic Gibbs measures for the Potts model on the Cayley tree. – Moscow, Russia: Theor Math Phys 2013 b;175:699–709
