Date: 22nd August (Thursday), 2024
Place: #702, Natural Science Building, Hanyang University

Time: July 25nd (Thursday) 10:30
Place: Natural Science Building #744
Speaker: Prof. Woojoo Shim (Kyungpook National University)

Title: Synchronization estimate of the discrete Kuramoto model with multiplicative random noise

Abstract:
In this talk, we study the emergence of synchronization of time-discretization of the Kuramoto model with multiplicative noise. First, we will briefly describe several methods for approximating the solution of stochastic differential equations, including the method we used in the paper. Then, we introduce the existing results of the continuous-time stochastic Kuramoto model and the discrete-time deterministic Kuramoto model. Finally, we will discuss a sufficient condition that guarantees the identical oscillators in the discrete-time Kuramoto model with multiplicative noise are asymptotically synchronized almost surely.

1.
Time: May 22nd (Wednesday) 10:30
Place: Natural Science Building #744
Speaker: Jaeyoung Yoon (Seoul National University)

Title: Measure-valued death state and local sensitivity analysis for Winfree model with uncertain high-order couplings

Abstract:
We study the measure-valued death state and local sensitivity analysis of the Winfree model and its mean-field counterpart with uncertain high-order couplings. The Winfree model is the first mathematical model for synchronization, and it can be cast as the effective approximation of the pulse-coupled model for synchronization, and it exhibits diverse asymptotic patterns depending on system parameters and initial data. For the proposed models, we present several frameworks leading to oscillator death in terms of system parameters and initial data, and the propagation of regularity in random space.

2.
Time: May 29th (Wednesday) 10:30
Place: Natural Science Building #744
Speaker: Dr. Seonwoo Kim (Korea Institute for Advanced Study)

Title: Hierarchical metastability structure in the reversible inclusion process

Abstract:
In this talk, I will discuss the hierarchical decomposition of metastability, which is ubiquitous in stochastic dynamical systems with complicated energy landscapes, and in particular the mechanism that triggers such a multi-scale phenomenon. Then, to fix ideas, I will focus on a specific example, the reversible inclusion process on a finite graph, where the hierarchical structure is based on the graph distance between the sites with maximum invariant measure. Then, I will briefly sketch the idea of proofs for the main theorems.

Date: August 29th(Monday)

Organizer:
박진영 Jinyeong Park (Hanyang University)

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Time: July 8th (Friday) 10:30
Place: Natural Science Building #702
Speaker: Dr. Myeongju Kang (Seoul National University)

Title: Asymptotic behavior of various synchronization models and their continuum limit

Abstract:
Synchronous behaviors of oscillatory complex systems are ubiquitous in many biological and chemical systems, to name a few, firing of fireflies, synchronization of metronomes, rhythmic beating of pacemaker cells, etc. Famous examples are the Kuramoto model, which is a phase-coupled model, and the Winfree model, which is a pulse-coupled model. Both ode systems describe the time-evolutionary behavior of oscillators on one dimensional torus. Continuum limit is an effective approximation to describe a system with infinitely many particles using integro-differential equation.
In this talk, we first study the emergent dynamics of the particle models. Since solutions of the particle models become simple function valued solutions of the continuum models, analytical results on the time-evolutionary behavior of the particle models can be applied to analyze the continuum models. Especially, we study in what sense sequences of simple functions obtained from the particle models converge to solutions of the continuum models.

Date: July 18th(Monday) – 20th(Wednesday)

Organizers:
김승혁 Seunghyeok Kim, 박진영 Jinyeong Park

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