On a Mathematical Model of Biological Self-Organization

被引：0

作者：

A. Yu. Kolesov

N. Kh. Rozov

V. A. Sadovnichii

机构：

[1] P. G. Demidov Yaroslavl State University,

[2] Moscow State University,undefined

来源：

Proceedings of the Steklov Institute of Mathematics | 2019年 / 304卷

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D O I：

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摘要：

A system of two generalized Hutchinson’s equations coupled by linear diffusion terms is considered. It is established that for an appropriate choice of parameters, the system has a stable relaxation cycle whose components turn into each other under a certain phase shift. A number of additional properties of this cycle are presented that allow one to interpret it as a self-organization mode.

引用

页码：160 / 189

页数：29

共 16 条

[1]

van der Pol B(1926)On ‘relaxation-oscillations’ Philos. Mag. J. Sci., Ser. 7 2 978-992

[2]

Zheleztsov N A(1948)Self-modulation of self-oscillations of a vacuum-tube oscillator with automatic bias in the cathode loop Zh. Tekh. Fiz. 18 495-509

[3]

Mishchenko E F(1955)Periodic solutions of systems of differential equations that are close to discontinuous solutions Dokl. Akad. Nauk SSSR 102 889-891

[4]

Pontryagin L S(1948)Circular causal systems in ecology Ann. N.Y. Acad. Sci. 50 221-246

[5]

Hutchinson G E(2012)Discrete autowaves in systems of delay differential-difference equations in ecology Proc. Steklov Inst. Math. 277 94-136

[6]

Kolesov A Yu(2013)Relaxation self-oscillations in Hopfield networks with delay Izv. Math. 77 271-312

[7]

Rozov N Kh(2013)Periodic traveling-wave-type solutions in circular chains of unidirectionally coupled equations Theor. Math. Phys. 175 499-517

[8]

Glyzin S D(2014)The buffer phenomenon in ring-like chains of unidirectionally connected generators Izv. Math. 78 708-743

[9]

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[10]

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