scholarly journals On the Global Character of the System of Piecewise Linear Difference Equations xn+1=|xn|−yn−1 and yn+1=xn−|yn|

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Wirot Tikjha ◽  
Yongwimon Lenbury ◽  
Evelina Giusti Lapierre
Keyword(s):  
Difference Equations ◽  
Piecewise Linear ◽  
Linear Difference Equations ◽  
Global Character

scholarly journals On the Global Character of the System of Piecewise Linear Difference Equations and

2010 ◽  
Vol 2010 (1) ◽  
pp. 573281 ◽  
Author(s):  
Wirot Tikjha ◽  
Yongwimon Lenbury ◽  
EvelinaGiusti Lapierre
Keyword(s):  
Difference Equations ◽  
Piecewise Linear ◽  
Linear Difference Equations ◽  
Global Character

On n-dimensional piecewise-linear difference equations

1980 ◽  
Vol 4 (4) ◽  
pp. 715-731 ◽  
Author(s):  
Manuel Scarowsky ◽  
Abraham Boyarsky
Keyword(s):  
Difference Equations ◽  
Piecewise Linear ◽  
Linear Difference Equations

Nonlocality of one-dimensional bilinear hardening–softening elastoplastic axial lattices

2019 ◽  
Vol 25 (2) ◽  
pp. 475-497
Author(s):  
Vincent Picandet ◽  
Noël Challamel
Keyword(s):  
Difference Equations ◽  
Differential Operators ◽  
Scale Effects ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Continuous Model ◽  
Lattice System ◽  
Discrete Problem ◽  
Linear Difference Equations ◽  
One Dimensional

The static behaviour of an elastoplastic axial lattice is studied in this paper through both discrete and nonlocal continuum analyses. The elastoplastic lattice system is composed of piecewise linear hardening–softening elastoplastic springs connected between each other via nodes, loaded by concentrated tension forces. This inelastic lattice evolution problem is ruled by some difference equations, which are shown to be equivalent to the finite difference formulation of a continuous elastoplastic bar problem under distributed tension load. Exact solutions of this inelastic discrete problem are obtained from the resolution of this piecewise linear difference equations system. Localization of plastic strain in the first elastoplastic spring, connected to the fixed end, is observed in the softening range. A continuous nonlocal elastoplastic theory is then built from the lattice difference equations using a continualization process, based on a rational asymptotic expansion of the associated pseudo-differential operators. The continualized lattice-based model is equivalent to a distributed nonlocal continuous elastoplastic theory coupled to a cohesive elastoplastic model, which is shown to capture efficiently the scale effects of the reference axial lattice. The hardening–softening localization process of the nonlocal elastoplastic continuous model strongly depends on the lattice spacing, which controls the size of the nonlocal length scales. An analogy with the one-dimensional lattice system in bending is also shown. The considered microstructured elastoplastic beam is a Hencky bar-chain connected by elastoplastic rotational springs. It is shown that the length scale calibration of the nonlocal model strongly depends on the degree of the difference equations of each lattice model (namely axial or bending lattice). These preliminary results valid for one-dimensional systems allow possible future developments of new nonlocal elastoplastic models, including two- or even three-dimensional elastoplastic interactions.

scholarly journals Global and Local Behavior of the System of Piecewise Linear Difference Equations xn+1 = |xn| − yn − b and yn+1 = xn − |yn| + 1 Where b ≥ 4

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1390
Author(s):  
Busakorn Aiewcharoen ◽  
Ratinan Boonklurb ◽  
Nanthiya Konglawan
Keyword(s):  
Periodic Solution ◽  
Equilibrium Point ◽  
Difference Equations ◽  
Piecewise Linear ◽  
Global Behavior ◽  
Local Behavior ◽  
Linear Difference Equations ◽  
All Solutions ◽  
Prime Period ◽  
Global And Local

The aim of this article is to study the system of piecewise linear difference equations xn+1=|xn|−yn−b and yn+1=xn−|yn|+1 where n≥0. A global behavior for b=4 shows that all solutions become the equilibrium point. For a large value of |x0| and |y0|, we can prove that (i) if b=5, then the solution becomes the equilibrium point and (ii) if b≥6, then the solution becomes the periodic solution of prime period 5.

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