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[CT053]

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : we propose a new family of one-dimensional smooth maps based on the Gaussian function exhibiting robust chaos in a wide range of parameter space. We prove the existence of robust chaos in the proposed family of maps using the stability criterion and extensive numerical computation of the Lyapunov exponent and sample entropy. We also present other important properties such as the bifurcation phenomenon, invariant measure, ergodicity, entropy and other statistical properties of the proposed robust chaos map.
Classification : 37M05, 37M20, 37M25, 65P40
Author(s) :
- Vinod Patidar (Sir Padampat Singhania University)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : Attractors arising from delay embedded time-series can characterise system dynamics. However, extracting useful representations is challenging for systems with high-dimensional or complex structure. We propose a data-driven method to represent attractors as networks, where dynamics are encoded as node transition probabilities. The usefulness of this representation is demonstrated in two tasks: (1) surrogate data generation; and (2) change point detection. These methods are applied to chaotic time-series, and experimental ECG data for heart attack detection.
Classification : 37M10, 37M22, 94C12
Author(s) :
- Eugene Tan (The University of Western Australia)
- Shannon Dee Algar (The University of Western Australia)
- Debora Correa (The University of Western Australia)
- Thomas Stemler (The University of Western Australia)
- Michael Small (The University of Western Australia)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : We focus on a max-plus discretized model that is identified with the Lozi map in this talk. The max-plus model can be derived from the generalized Sel’kov model composed of non-linear differential equations via tropical discretization and ultradiscretization. Based on the Poincare mapping method and the estimation of Lyapunov exponents, the dynamical properties of the max-plus model and its transformation from the generalized Sel’kov model are discussed.
Classification : 37M20, 37M15, 65P40, 68Q80, 37J70
Author(s) :
- Shousuke Ohmori (Waseda University)
- Yoshihiro Yamazaki (Waseda University)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : We focus on limit cycles of discretized Sel'kov model derived from continuous Sel'kov model via tropical discretization. The discretized model possesses a parameter for time step. We numerically found, by varying the parameter, that density profile of phase in the limit cycles transits between continuous and ultradiscrete, and that the ultradiscrete state corresponds to a max-plus dynamical system. In this talk, we discuss these findings from the viewpoint of nonlinear dynamical systems.
Classification : 37M20, 37M15, 65P40, 68Q80, 37J70, ultradiscretization, max-plus dynamical system, bifurcation
Author(s) :
- Yoshihiro Yamazaki (Waseda University)
- Shousuke Ohmori (Waseda University)

Session Date & Time : 2E (Aug.22, 17:40-19:20)
Type : Contributed Talk
Abstract : We study stochastic convergence of the discrete Consensus-Based Optimization, called CBO algorithm, in almost-sure sense and in expectation. CBO is a mathematical toy example for non-gradient multi-point optimizer which tries to find the global minimum point of a given cost function. The convergence analysis guarantees the termination of the optimization process. The main result is a joint work with Seung-Yeal Ha, Shi Jin, and Doheon Kim.
Classification : 37M99, 65p99
Author(s) :
- Dongnam Ko (The Catholic University of Korea)