Chaotic gas turbine subject to augmented Lorenz equations

Symbolic diffusion entropy rate of chaotic time series as a surrogate measure for the largest Lyapunov exponent

Existing methods for estimating the largest Lyapunov exponent from a time series rely on the rate of separation of initially nearby trajectories reconstructed from the time series in phase space. According to Ueda, chaotic dynamical behavior is viewed as a manifestation of random transitions between unstable periodic orbits in a chaotic attractor, which are triggered by perturbations due to experimental observation or the roundoff error characteristic of the computing machine, and consequently consists of a sequence of piecewise deterministic processes instead of an entirely deterministic process. Chaotic trajectories might have no physical reality. Here, we propose a mathematical method for estimating a surrogate measure for the largest Lyapunov exponent on the basis of the random diffusion of the symbols generated from a time series in a chaotic attractor, without resorting to initially nearby trajectories. We apply the proposed method to numerical time series generated by chaotic flow models and verify its validity.

Nonlinear dynamics of a buoyancy-induced turbulent fire

We conduct a numerical study on the dynamic behavior of a buoyancy-induced turbulent fire from the viewpoints of symbolic dynamics, complex networks, and statistical complexity. Here, we consider two classes of entropies: the permutation entropy and network entropy in ε-recurrence networks, both of which evaluate the degree of randomness in the underlying dynamics. These entropies enable us to capture the significant changes in the dynamic behavior of flow velocity fluctuations. The possible presence of two important dynamics, low-dimensional deterministic chaos in the near field dominated by the motion of large-scale vortices and high-dimensional chaos in the far field forming a well-developed turbulent plume, is clearly identified by the multiscale complexity-entropy causality plane.