We focus on an SU(N ) Yang-Mills gauge theory in 0 + 1-dimensions with the same matrix content as the bosonic part of the BFSS matrix model, but with mass deformation terms breaking the global SO(9) symmetry of the latter to SO(5) × SO(3) × ℤ2. Introducing an ansatz configuration involving fuzzy four and two spheres with collective time dependence, we examine the chaotic dynamics in a family of effective Lagrangians obtained by tracing over the aforementioned ansatz configurations at the matrix levels $$ N=\frac{1}{6} $$ N = 1 6 (n + 1)(n + 2)(n + 3), for n = 1, 2, · · · , 7. Through numerical work, we determine the Lyapunov spectrum and analyze how the largest Lyapunov exponents(LLE) change as a function of the energy, and discuss how our results can be used to model the temperature dependence of the LLEs and put upper bounds on the temperature above which LLE values comply with the Maldacena-Shenker-Stanford (MSS) bound 2πT , and below which it will eventually be violated.

We introduce a new type of chaos synchronization, specifically the delta synchronization of Poincaré chaos. The method is demonstrated for the irregular dynamics in coupled gas discharge-semiconductor systems (GDSSs). It is remarkable that the processes are not generally synchronized. Our approach entirely relies on ingredients of the Poincaré chaos, which in its own turn is a consequence of the unpredictability in Poisson stable motions. The drive and response systems are in the connection, such that the latter is processed through the electric potential of the former. The absence of generalized synchronization between these systems is indicated by utilizing the conservative auxiliary system. However, the existence of common sequences of moments for finite convergence and separation confirms the delta synchronization. This can be useful for complex dynamics generation and control in electromagnetic devices. A bifurcation diagram is constructed to separate stable stationary solutions from non-trivial oscillatory ones. Phase portraits of the drive and response systems for a specific regime are provided. The results of the sequential test application to indicate the unpredictability and the delta synchronization of chaos are demonstrated in tables. The computations of the dynamical characteristics for GDSSs are carried out by using COMSOL Multiphysics version 5.6 and MATLAB version R2021b.

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