Japan Journal of Industrial and Applied Mathematics 35 939-968 Jul 2018 [Refereed]

? 2018, The Author(s). One parameter family of rectangular periodic traveling wave solutions are known to exists in a perturbed system of the modified KdV equation. The rectangular periodic traveling wave consists basically of front and back trans...

? 2018 We consider a two-variable partial differential equations model of cardiac excitation and study spiral wave instability in a one-parameter family of solutions. We investigate numerically the existence of periodic traveling wave solution and...

Ekeoma R. Ijioma, Hirofumi Izuhara, Masayasu Mimura, Toshiyuki Ogawa

Combustion and Flame 162 Jan 2017 [Refereed]

? 2015 The Combustion Institute. The present study concerns the homogenization and fingering instability of a microgravity smoldering combustion problem with radiative heat transfer. The major premise of the homogenization procedure is the slow ex...

M. Osman Gani, M. Osman Gani, M. Osman Gani, Toshiyuki Ogawa

Communications in Nonlinear Science and Numerical Simulation 33 30-42 Jan 2016 [Refereed]

? 2015 Elsevier B.V. We study the two-component Aliev-Panfilov reaction-diffusion system of cardiac excitation. It is known that the model exhibits spiral wave instability in two-dimensional spatial domains. In order to describe the spiral wave in...

Springer Proceedings in Mathematics and Statistics 183 531-562 Jan 2016 [Refereed]

? Springer Japan 2016. The dynamics and bifurcation structure of the normal form in the presence of 0:1:2 resonance are studied. It is proved that connecting orbits (heteroclinic cycles or homoclinic orbits) exist on the center manifold of the nor...

East Asian Journal on Applied Mathematics 5 138-149 May 2015 [Refereed]

? 2015 Global-Science Press. We numerically study a thermal-diffusive model for smouldering combustion under microgravity with convective heat losses. In accordance with previous experimental observations, it is well known that porous materials bu...

Applied Mathematics and Computation 256 968-984 Apr 2015 [Refereed]

? 2015 Elsevier Inc. All rights reserved. We introduce a two-variable system of reaction-diffusion equations for excitable media. We numerically investigate the existence and stability of periodic traveling wave solutions in a two-dimensional para...

? 2015 Elsevier Ltd. All rights reserved. Autonomous pattern formation phenomena are ubiquitous throughout nature. The goal of this paper is to show the possibility to effectively generate various desired spatial patterns by guiding such phenomena...

Ekeoma Rowland Ijioma, Adrian Muntean, Toshiyuki Ogawa, Toshiyuki Ogawa

International Journal of Heat and Mass Transfer 81 924-938 Jan 2015 [Refereed]

? 2014 Elsevier Ltd. All rights reserved. It is well known from experiments that a sample of thin porous material burning against an oxidizing air under microgravity exhibits various finger-like char patterns. The patterns are classified into thre...

Tasnim Fatima, Ekeoma Ijioma, Toshiyuki Ogawa, Adrian Muntean

Networks and Heterogeneous Media 9 709-737 Jan 2014 [Refereed]

? American Institute of Mathematical Sciences. We study the homogenization of a reaction-diffusion-convection system posed in an ε-periodic δ-thin layer made of a two-component (solid-air) composite material. The microscopic system includes heat o...

Proceedings of the American Control Conference 3759-3764 Sep 2013 [Refereed]

In this paper, we formulate and solve feedback stabilization problem of unstable non-uniform spatial pattern in reaction-diffusion systems. By considering spatial spectrum dynamics, we obtain a finite dimensional approximation that takes over the ...

Ekeoma Rowland Ijioma, Adrian Muntean, Toshiyuki Ogawa

Combustion Theory and Modelling 17 185-223 Apr 2013 [Refereed]

The development of fingering char patterns on the surface of porous thin materials has been investigated in the framework of reverse combustion. This macroscopic characteristic feature of combustible media has also been studied experimentally and ...

Networks and Heterogeneous Media 7 893-926 Dec 2012 [Refereed]

Oscillatory dynamics in a reaction-diffusion system with spatially nonlocal effect under Neumann boundary conditions is studied. The system provides triply degenerate points for two spatially non-uniform modes and uniform one (zero mode). We focus...

Discrete and Continuous Dynamical Systems 25 273-297 Sep 2009 [Refereed]

Bifurcation structure of the stationary solutions to the Swift-Hohenberg equation with a symmetry breaking boundary condition is studied. Namely, a SO(2) breaking perturbation is added to the Neumann or Dirichlet boundary conditions. As a result, ...

Journal of Mathematical Biology 58 459-479 Mar 2009 [Refereed]

In this paper, a mathematical model of a prey-predator system is proposed to resolve the paradox of enrichment in ecosystems. The model is based on the natural strategy that a predator takes, i.e, it produces resting eggs in harsh environment. Our...

Chemical Physics Letters 453 35-39 Aug 2008 [Refereed]

Experimental and theoretical studies for bistability between spatially uniform and non-uniform electrochemical oscillations are performed, by taking a current oscillation of N-NDR type, appearing in H2O2 reduction on platinum (Pt) ring electrodes,...

Journal of Chemical Physics 128 Jan 2008 [Refereed]

The pattern selection principle for various modes of spatially nonuniform oscillation was investigated by taking a current oscillation of negative differential resistance type, appearing in H2 O2 reduction on platinum (Pt) ring electrodes, as a mo...

In this paper, we consider the Swift-Hohenberg equation with perturbed boundary conditions. We do not a priori know the eigenfunctions for the linearized problem since the SO(2) symmetry of the problem is broken by perturbation. We show that how t...

Journal of Computational and Applied Mathematics 199 238-244 Feb 2007 [Refereed]

In this paper, localized patterns of the quintic Swift-Hohenberg equation are studied. A numerical verification method with the Conley index theory developed in Zgliczy?ski and Mischaikow [Rigorous numerics for partial differential equations: the ...

Communications on Pure and Applied Analysis 5 383-393 Jun 2006 [Refereed]

Rayleigh-Benard convection in a small rectangular domain is studied by the standard bifurcation analysis. The dynamics on the center manifold is calculated up to 3rd order. By this normal form, it is possible to determine the local bifurcation str...

Sarah Day, Yasuaki Hiraoka, Konstantin Mischaikow, Toshiyuki Ogawa

SIAM Journal on Applied Dynamical Systems 4 1-31 Dec 2005 [Refereed]

This paper presents a rigorous numerical method for the study and verification of global dynamics. In particular, this method produces a conjugacy or semiconjugacy between an attractor for the Swift-Hohenberg equation and a model system. The proce...

Japan Journal of Industrial and Applied Mathematics 22 57-75 Jan 2005 [Refereed]

Localized patterns of the quintic Swift-Hohenberg equation are studied by bifurcation analysis and rigorous numerics. First of all, fundamental bifurcation structures around the trivial solution are investigated by a weak nonlinear analysis based ...

Japan Journal of Industrial and Applied Mathematics 18 521-542 Jan 2001 [Refereed]

A family of periodic travelling wave solutions parameterized by the wavenumber is shown to bifurcate from the trivial solution in a perturbed KdV equation. Studying linearized eigenvalue problem about each periodic travelling wave solution, all of...

SIAM Journal on Applied Mathematics 57 485-500 Apr 1997 [Refereed]

An eigenvalue problem for the pulse solutions to perturbed generalized Korteweg-de Vries equations is studied. Evans-function techniques with the aid of the geometric approach to singular perturbation problems are employed. This approach leads to ...

Physica D: Nonlinear Phenomena 108 277-290 Jan 1997 [Refereed]

Interactions of two-dimensional solitary waves of the Benney equation are investigated by a formal asymptotic analysis: reduction to a system of ordinary differential equations (ODEs) which describes the motion of the pulse positions. After the fo...

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik 76 633-634 Dec 1996 [Refereed]

The Eigenvalue problem for the pulse solutions to perturbed generalized Korteweg-de Vries equations is studied. Evans function techniques with the aid of a geometric approach to singular perturbation problems are employed. The results lead to a cl...

Japan Journal of Applied Mathematics 7 255-276 Jun 1990 [Refereed]

We show the existence of travelling wave solutions to a generalized system of nerve equations which include the case where the slow variable also has a diffusion effect. We are mainly interested in the persistency of the pulse solution of the Fitz...