| Budget Amount *help |
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1995: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1994: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Research Abstract |
We have investigated the spatio-temporal pattern in a Bonhoeffer-van der Pol (BVP) type reaction- diffusion system. This study was motivated from the peculiar behavior observed unexpectedly in computer simulations of pulse collision. That is, a pair propagating pulses do not annihilate upon collision but constitute a domain which emits outgoing pulses persistently. This provides us with anti-example that pulses in a dissipative system simply disappear upon collision. We call this phenomenon a self-organized pulse generator. Although BVP equation had been studied for more than twenty years, the above property had not been reported.
In our study, we have obtained the following facts. The origin of the pulse generator is the bistability such that a uniform solution and a limit cycle coexist. Furthermore, the excitability of the system and the bistability cause a variety of spatio-temporal patterns. The phase diagram is obtained by changing the parameters of oscillatory strength and excitability. In two dimensions, a target pattern is formed by the pulse generator. If one increases the diffusion constant, the target pattern becomes extended, localized and finally motionless.
As a related problem, we have also studied domain motion in a BVP-type system with one activator and two inhibitors. The interface dynamics associated with computer simulations provides us with the condition of breathing, wiggling and chaotic motion of domains. We have shown that the wiggling motion appears in a wider parameter region than the breathing motion.
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