Analysis of fractional order Bonhoeffer-van der Pol oscillator

Gafiychuk V; Datsko B; Meleshko V

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Analysis of fractional order Bonhoeffer-van der Pol oscillator

机译：分数阶Bonhoeffer-van der Pol振荡器的分析

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We investigate a Bonhoeffer-van der Pol dynamical system with fractional derivatives of different orders. Spectral analysis is fulfilled analytically for certain relationships between derivative orders and numerically for any relation between them. It is shown that such a system could be more unstable than the system with integer derivatives even for fractional order indices less than one. Different types of oscillations appear as a result of this instability. Computer simulation of the typical oscillations demonstrating the observed effects are performed. (C) 2007 Elsevier B.V. All rights reserved.

机译：我们研究具有不同阶数分数导数的Bonhoeffer-van der Pol动力学系统。对于导数阶之间的某些关系，在解析上实现了频谱分析，对于它们之间的任何关系，在数值上实现了频谱分析。结果表明，即使分数阶索引小于1，这种系统也可能比具有整数导数的系统更不稳定。由于这种不稳定性，会出现不同类型的振荡。执行典型振动的计算机模拟，演示观察到的效果。（C）2007 Elsevier B.V.保留所有权利。

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《Physica, A. Statistical mechanics and its applications》 |2008年第3期|共7页
作者
Gafiychuk V; Datsko B; Meleshko V;
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正文语种 eng
中图分类理论物理学;
关键词
dynamical system; fractional differential equations; instability domain; oscillations; REACTION-DIFFUSION; SYSTEM; CHAOS;

机译：动力系统;分数阶微分方程;不稳定性域;振动;反应扩散;系统;CHAOS;

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Analysis of fractional order Bonhoeffer-van der Pol oscillator

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