Two Kinds Of Solutions To The FitzHugh-Nagumo Equations

^#) - ^IXSYER S THESIS Abstract This paper is concerned with the famous FitzHugh-Nagumo Equations { &ti a2u 1 ?u(1--u)(u?a)梩? (OO,³>O) and the existence of two kinds of traveling wave solution-traveling front and traveling pulse is proved.Letc x + ct,u?w, ayy ? whereæ•€ 0 d denotes 搤^?,(1 .6) is transformed into (III) &^u-yv I 741 ?u)(u ?a) + v ?cw Then,^ve can see that under some condition, (III)has a heteroclinic or homoclinic orbit.for special c> O,which implies that (1.6) has a traveling front solution or taveling pulse solution. In this paper,heteroclinic orbits of the following equations are firstly discussed (2.2) { 梪1)(ui 梐)+cwi C, = ?13(1 ?tL3)(tL3 ?a) + v3 + cw3 ?梫3 iii PER THESIS ?w4 I ?yv4) = 6 (2.6) C I C t = ?u¹)(u4 ?a) ?v4 ?梀4 ?cw4 67 Secondly, we compare some orbits of (III) with these orbits, Finally, the existence of heterodinic and homodinic orbits of (III) is proved by making use of supremum thereom The main results are theorem 3.1.4,3.1.5 and 4.1.2, of which theorem 3.1.4 and 3.1.5 show the existence of heteroclinic orbit of (III) for some c Co F (ce, c*). and theorem 4.1.2 shows the existence of homoclinic orbit of (III) for some c c00 F (ce, C0)...