TY - JOUR

T1 - On camel-like traveling wave solutions in cellular neural networks

AU - Hsu, Cheng Hsiung

AU - Yang, Suh Yuh

N1 - Funding Information:
*Corresponding author. Fax: +886-3-425-7379. E-mail addresses: [email protected] (Cheng-Hsiung Hsu), [email protected] (Suh-Yuh Yang). 1Partially supported by the National Science Council of Taiwan and the National Center for Theoretical Sciences, Mathematics Division, Taiwan. 2Partially supported by the National Science Council of Taiwan.

PY - 2004/1/20

Y1 - 2004/1/20

N2 - This paper is concerned with the existence of camel-like traveling wave solutions of cellular neural networks distributed in the one-dimensional integer lattice Z1. The dynamics of each given cell depends on itself and its nearest m left neighbor cells with instantaneous feedback. The profile equation of the infinite system of ordinary differential equations can be written as a functional differential equation in delayed type. Under appropriate assumptions, we can directly figure out the solution formula with many parameters. When the wave speed is negative and close to zero, we prove the existence of camel-like traveling waves for certain parameters. In addition, we also provide some numerical results for more general output functions and find out oscillating traveling waves numerically.

AB - This paper is concerned with the existence of camel-like traveling wave solutions of cellular neural networks distributed in the one-dimensional integer lattice Z1. The dynamics of each given cell depends on itself and its nearest m left neighbor cells with instantaneous feedback. The profile equation of the infinite system of ordinary differential equations can be written as a functional differential equation in delayed type. Under appropriate assumptions, we can directly figure out the solution formula with many parameters. When the wave speed is negative and close to zero, we prove the existence of camel-like traveling waves for certain parameters. In addition, we also provide some numerical results for more general output functions and find out oscillating traveling waves numerically.

KW - Camel-like traveling waves

KW - Cellular neural networks

KW - Lattice dynamical systems

KW - Oscillating traveling waves

UR - http://www.scopus.com/inward/record.url?scp=0742304053&partnerID=8YFLogxK

U2 - 10.1016/S0022-0396(03)00135-9

DO - 10.1016/S0022-0396(03)00135-9

M3 - 期刊論文

AN - SCOPUS:0742304053

SN - 0022-0396

VL - 196

SP - 481

EP - 514

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -