PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 364 276-286 2006年5月
We present a three-component model which could represent the reaction of the organism to pathogen invasion. A continuous-time (differential) model is constructed first. Its discrete analogue is then derived and is used for numerical simulations wh...
S Isojima   B Grammaticos   A Ramani   J Satsuma   
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 39(14) 3663-3672 2006年4月
We present a new ultradiscretization approach which can be applied to discrete systems, the solutions of which are not positive definite. This was made possible, thanks to an ansatz involving the hyperbolic-sine function. We apply this new procedu...
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 347 1-16 2005年3月
We present the discrete systems which result from the discrete Painlev equations q-P-VI and d-P-V associated to the affine Weyl group E-7((1)). Two different procedures ("limits" and "degeneracies") Lire used, giving rise to a host of new discrete...
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS 12 363-371 2005年1月
We present a novel method for the reduction of integrable two-dimensional discrete systems to one-dimensional mappings. The procedure allows for the derivation of nonautonomous systems, which are typically discrete (difference or q) Painleve equat...
M. Murata   J. Satsuma   A. Ramani   B. Grammaticos   
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 43(31) 2010年8月
We present a systematic approach to the construction of discrete analogues for differential systems. Our method is tailored to first-order differential equations and relies on a formal linearization, followed by a Pade-like rational approximation ...
A. Ramani   B. Grammaticos   J. Satsuma   R. Willox   
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 42(28) 282002 2009年7月
We examine two integrable discrete lattice equations obtained by Levi and Yamilov. We show that the first one is a form of the lattice KdV equation already obtained by Hirota and Tsujimoto, while the second one is a discrete form of mKdV. We prese...
A. Ramani   B. Grammaticos   J. Satsuma   R. Willox   
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 42(28) 282002 2009年7月
We examine two integrable discrete lattice equations obtained by Levi and Yamilov. We show that the first one is a form of the lattice KdV equation already obtained by Hirota and Tsujimoto, while the second one is a discrete form of mKdV. We prese...
A. Ramani   B. Grammaticos   J. Satsuma   
CHAOS SOLITONS & FRACTALS 40(1) 491-496 2009年4月
We present two models for an epidemic where the individuals are infective over it fixed period of time and which never becomes endemic i.e., no infective individuals remain after the epidemic has run its course. The first model is based oil it del...
A. Ramani   B. Grammaticos   J. Satsuma   
CHAOS SOLITONS & FRACTALS 40(1) 491-496 2009年4月
We present two models for an epidemic where the individuals are infective over it fixed period of time and which never becomes endemic i.e., no infective individuals remain after the epidemic has run its course. The first model is based oil it del...