- P(gun)]
һηǾϵy(tng)H0pfֲоՓ
ժҪоһПo(w)ǾԻ֏(f)ĎηǾϵy(tng)Hopβ톖(wn)}ȣ(yng)Lagrange̽ˎηǾԄ(dng)W(xu)\(yn)(dng)ַ̣ƽc(din)ķֲ(wn)Եȏ(f)s(dng)W(xu)О飬̩ռ(j)(sh)(du)ԭϵy(tng)ƽM(jn)ν?ci)࣬A.Van del Pol_(dng)õηǾLienardϵy(tng)ȻHopβՓõϵy(tng)ڷֲͻ׃c(din)(g)Hopβ棬ڷֲϣϵy(tng)ƽc(din)(wn)l(f)׃ƽc(din)F(xin)Oޭh(hun)
P(gun)I~ηǾϵy(tng)ηǾԣHopfֲOޭh(hun)Runge-Kutta
ηǾǮ(dng)ƌW(xu)g(sh)c̑(yng)н(jng)ҪǾأcϷǾԡ|ǾԘ(gu)ɹ̑(yng)оеǾԆ(wn)}ڟo(w)ǾԳF(xin)һµĎηǾԄ(dng)ϵy(tng)ԓϵy(tng)SDSmooth anddiscontinuousӼSDӣԓهϵy(tng)(sh)F(xin)⻬(dng)W(xu)Bm(x)(dng)W(xu)D(zhun)wԡ
оǾVan del Pol_(dng)SDӵHopfֲՓõϵy(tng)ĶHopfֲО飬(sh)ֵģM(yn)CηǾϵy(tng)ĶOޭh(hun)F(xin)
1.ηǾԄ(dng)W(xu)ϵy(tng)
1.1W(xu)ģ
SDW(xu)ģͣ҂ˎηǾԄ(dng)W(xu)ϵy(tng)SDӣW(xu)ģͣһ(g)|(zh)KmB|(zh)Kһ(du)Aб܉Ϙ(gu).ɵĄϵ(sh)ȻL(zhng)ȷքekLĩ˹̶һ(g)ԵϣmȻṩԻ؏(f)ģ͎ηǾԘ(gu)͵ĸ׃ʹ|(zh)KϵˮƽF(xin)鏊(qing)o(w)Ǿԡ
2.ηǾϵy(tng)\(yn)(dng)ַ̞
HopfֲՓоϵy(tng)ƽc(din)ֲa(chn)(wn)B(ti)ڽĆ(wn)}˼ǻڽ(jng)䷀(wn)Փķ̵Ĕz(dng)ⷀ(wn)ԁ(li)Єeƽc(din)ķ(wn).HopfCϵy(tng)ڷֲֵ̎ƽc(din)ֲһ(g)dzڽ⣬(du)(yng)ϵy(tng)ĘOޭh(hun)ϵy(tng)l(f)ʎʎʧ(wn)ۙϵy(tng)ƽΡ_ֲc(din)λã(du)˽o(w)Ǿϵy(tng)(wn)Լ׃Ҏ(gu)Ҫx
3.Y(ji)Z(y)
·δ_(dng)ηǾϵy(tng)Ĺ⻬cBm(x)(dng)W(xu)D(zhun)wԣƽc(din)ֲ֏(f)(sh)ܺ(sh)oVander Pol_(dng)ϵy(tng)HoDfֲ?xing)l.ՓY(ji)ηǾϵy(tng)Hopfֲ(wn)ԵĿcO(sh)Ӌ(j)(sh)xȡṩՓ(j)
һηǾϵy(tng)H0pfֲоՓġP(gun)£
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