Mathematical modeling of traveling autosolitons in fractional-order activator-inhibitor systems

• Autorzy: Datsko B. , Gafiychuk V.

Identyfikatory

DOI

10.24425/124256

• Języki publikacji: EN

Abstrakty

EN

In the article, basic properties of traveling spatially nonhomogeneous auto-wave solutions in nonlinear fractional-order reactiondiffusion systems are investigated. Such solutions, called autosolitons, arise in a stability region of the system and can coexist with the spatially homogeneous states. By a linear stability analysis and computer simulation, it is shown that the order of the fractional derivative can substantially change the properties of such auto-wave solutions and significantly enrich nonlinear system dynamics. The results of the linear stability analysis are confirmed by computer simulations of the generalized fractional van der Pol-FitzHugh-Nagumo model. A common picture of traveling auto-waves including series in time-fractional two-component activator-inhibitor systems is presented. The results obtained in the article for the distributed system have also been of interest for nonlinear dynamical systems described by fractional ordinary differential equations.

Słowa kluczowe

EN

fractional derivative; nonlinear dynamics; instability; autosoliton

PL

pochodna ułamkowa; dynamika nieliniowa; niestabilność

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2018
• Tom: Vol. 66, nr 4
• Strony: 411--418
• Opis fizyczny: Bibliogr. 35 poz., wykr.

Twórcy

autor

Datsko B.

• Rzeszow University of Technology, 8 Powstancow Warszawy St., 35-959 Rzeszow, Poland

autor

Gafiychuk V.

• Institute of Applied Problems of Mechanics and Mathematics NAS of Ukraine, 3b Naukova St., 79060 Lviv, Ukraine

Bibliografia

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).