Registered Data

[CT027]

  • Session Time & Room
    • CT027 (1/1) : 1C @G501 [Chair: Siwen Deng]
  • Classification
    • CT027 (1/1) : Qualitative properties of solutions to partial differential equations (35B) / Model systems in control theory (93C)

[02184] Oscillatory Translational Instability of Localized Spot Patterns in the Schnakenberg Reaction-Diffusion System in Defected 3D Domains

  • Session Time & Room : 1C (Aug.21, 13:20-15:00) @G501
  • Type : Contributed Talk
  • Abstract : For a two-component reaction-diffusion system in a bounded $3D$ domain, we investigate oscillatory instabilities of $N$-spot equilibrium. An $N$-spot equilibrium consists of localized spots in which the activator concentration is exponentially small everywhere except localized regions. In the stability analysis, we consider the translation mode and obtain the eigenvalue $\lambda$ is $\mathcal{O}(\varepsilon^2)$, which is the same order as the spot dynamics, while $\tau $ is $\mathcal{O}(\varepsilon^{-3})$. As a result, the system which contains the behavior of $\lambda$ and $\tau \lambda$ falls into the $\mathcal{O}(\varepsilon^2)$ correction. We later find that stability of these solutions is governed by a $3N \times 3N$ nonlinear matrix eigenvalue problem. Entries of the $3N \times 3N$ matrix involves terms calculated from certain Green’s function that contains information about the domain’s geometry. In the nonlinear matrix eigenvalue system, the most unstable eigenvalue decides the oscillation frequency at onset while the corresponding eigenvector determines the mode of spot oscillations. Further, we demonstrate the impact of various types of localized heterogeneity on this instability. An example of localized domain defects that we consider is to analyze the effect of perturbing the system by removing a small ball in the domain, which therefore allows a leakage of the chemical species out of the domain. Perturbation techniques is employed to compute Green’s function of near-spherical and near-cubic domains to gain analytic insight into how domain geometry select the dominant mode of oscillation. We show full solutions of the $3$-$D$ Schnakenberg PDE to confirm our asymptotic results.
  • Classification : 35B36, 35B35, 35B25
  • Format : Talk at Waseda University
  • Author(s) :
    • Siwen Deng (Macquarie University)
    • Justin Tzou (Macquarie University)

[02006] Dynamics of localization patterns in some nonlocal evolution equations

  • Session Time & Room : 1C (Aug.21, 13:20-15:00) @G501
  • Type : Contributed Talk
  • Abstract : Recently, studies have been proposed to simplify biological pattern formation problems by using nonlocal evolution equations to capture the self-organization caused by complex interactions with many factors. Especially, it has been reported that linear reaction-diffusion networks reduce to some nonlocal evolution equations reproducing patterns. Also, nonlocal effects are derived to reduce the structure of the network. In this talk, we report the influence of nonlocal effects on pattern dynamics for this reduced equation.
  • Classification : 35B36, 92C15, 35K57
  • Format : Talk at Waseda University
  • Author(s) :
    • Hiroshi Ishii (Kyoto University)

[00956] Inner Structure of Attractors for a Nonlocal Chafee-Infante Problem

  • Session Time & Room : 1C (Aug.21, 13:20-15:00) @G501
  • Type : Contributed Talk
  • Abstract : The structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion equation in which we cannot guarantee the uniqueness of the Cauchy problem is studied. The existence and properties of stationary points are analysed. Also, the study of the stability and connections between them are carried out, establishing that the semiflow is a dynamic gradient. As a consequence, the attractor consists of the stationary points and their heteroclinic connections.
  • Classification : 35B40, 35B41, 35B51, 35K55, 35K57
  • Format : Online Talk on Zoom
  • Author(s) :
    • RUBEN CABALLERO (UNIVERSIDAD MIGUEL HERNANDEZ DE ELCHE)

[00495] Input-state finite time stabilization of singular Markov fuzzy system.

  • Session Time & Room : 1C (Aug.21, 13:20-15:00) @G501
  • Type : Contributed Talk
  • Abstract : This work aims to examine the problem of Input-state finite-time stabilization of singular Markov T-S fuzzy systems with input time delay and disturbance. The sampled-data control for a singular Markov T-S fuzzy system with the quantized state has been designed. Using Lyapunov stability theory and linear matrix inequalities we guarantee that the singular fuzzy system is Input state Finite time stable. Finally, a numerical example is used to show the effectiveness of the proposed method.
  • Classification : 93CXX, 37MXX, 37N35, 34H05, 34H15
  • Format : Online Talk on Zoom
  • Author(s) :
    • Keerthana N (Anna University )

[01539] Actuator fault reconstruction-based tracking control for periodic piecewise polynomial systems

  • Session Time & Room : 1C (Aug.21, 13:20-15:00) @G501
  • Type : Contributed Talk
  • Abstract : The problem of actuator fault reconstruction and fault-tolerant tracking control for periodic piecewise polynomial systems with time-varying delay is investigated. The observer system is configured with periodic piecewise polynomial character to concurrently reconstruct the actuator faults and states of the system. Based on these configurations, the fault-tolerant tracking control is proposed, which aids in tracking the reference system by compensating the actuator faults. Numerical example is provided to validate the competence of proposed control scheme.
  • Classification : 93CXX, 37MXX, 37N35, 34H05, 34H15
  • Author(s) :
    • Aravinth Narayanan (Bharathiar University)
    • Sakthivel Rathinasamy (Bharathiar University)