Kanako Suzuki

Instability of turing patterns in reaction-diffusion-ODE systems

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.

Weak limit theorem for a nonlinear quantum walk

This paper continues the study of large time behavior of a nonlinear quantum walk begun in Maeda et al. (Discrete Contin Dyn Syst 38:3687–3703, 2018). In this paper, we provide a weak limit theorem for the distribution of the nonlinear quantum walk. The proof is based on the scattering theory of the nonlinear quantum walk, and the limit distribution is obtained in terms of its asymptotic state.

Coherence effect on chaos synchronization in optical fiber ring resonator system

Coherence effect on slave-slave type chaos synchronization system using optical fiber ring resonator is investigated numerically. The spectral width less than 1.0[ MHz] in the input light coherence is required for the reasonable chaos synchronization.

Message modulation type secure communication characteristics using optical fiber ring resonator chaos

Message modulation type chaos secure communication system using optical fiber ring resonators is analyzed numerically. It is found that the decryption characteristics improve up to the noise level with a decrease in the parameter difference.