TY - JOUR

T1 - Wave propagation in RTD-based cellular neural networks

AU - Hsu, Cheng Hsiung

AU - Yang, Suh Yuh

N1 - Funding Information:
Keywords: Lattice dynamical systems; RTD-based cellular neural networks; Discrete Fisher equation; Discrete Nagumo equation; Monotone iteration methods; Traveling waves; Standing waves *Corresponding author. Fax: +886-3-425-7379. E-mail addresses: chhsu@math.ncu.edu.tw (C.-H. Hsu), syyang@math.ncu.edu.tw (S.-Y. Yang). 1The work of this author was partially supported by the National Science Council of Taiwan, the National Center for Theoretical Sciences, Mathematics Division, Taiwan, and the Brain Research Center of University System of Taiwan. 2The work of this author was partially supported by the National Science Council of Taiwan and the Brain Research Center of University System of Taiwan.

PY - 2004/9/20

Y1 - 2004/9/20

N2 - This work investigates the existence of monotonic traveling wave and standing wave solutions of RTD-based cellular neural networks in the one-dimensional integer lattice Z1. For nonzero wave speed c, applying the monotone iteration method with the aid of real roots of the corresponding characteristic function of the profile equation, we can partition the parameter space (γ,δ)-plane into four regions such that all the admissible monotonic traveling wave solutions connecting two neighboring equilibria can be classified completely. For the case of c=0, a discrete version of the monotone iteration scheme is established for proving the existence of monotonic standing wave solutions. Furthermore, if γ or δ is zero then the profile equation for the standing waves can be viewed as an one-dimensional iteration map and we then prove the multiplicity results of monotonic standing waves by using the techniques of dynamical systems for maps. Some numerical results of the monotone iteration scheme for traveling wave solutions are also presented.

AB - This work investigates the existence of monotonic traveling wave and standing wave solutions of RTD-based cellular neural networks in the one-dimensional integer lattice Z1. For nonzero wave speed c, applying the monotone iteration method with the aid of real roots of the corresponding characteristic function of the profile equation, we can partition the parameter space (γ,δ)-plane into four regions such that all the admissible monotonic traveling wave solutions connecting two neighboring equilibria can be classified completely. For the case of c=0, a discrete version of the monotone iteration scheme is established for proving the existence of monotonic standing wave solutions. Furthermore, if γ or δ is zero then the profile equation for the standing waves can be viewed as an one-dimensional iteration map and we then prove the multiplicity results of monotonic standing waves by using the techniques of dynamical systems for maps. Some numerical results of the monotone iteration scheme for traveling wave solutions are also presented.

KW - Discrete Fisher equation

KW - Discrete Nagumo equation

KW - Lattice dynamical systems

KW - Monotone iteration methods

KW - RTD-based cellular neural networks

KW - Standing waves

KW - Traveling waves

UR - http://www.scopus.com/inward/record.url?scp=4344701434&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2004.02.008

DO - 10.1016/j.jde.2004.02.008

M3 - 期刊論文

AN - SCOPUS:4344701434

SN - 0022-0396

VL - 204

SP - 339

EP - 379

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -