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Bistable labyrinth-like structures and chimera states in a 2D lattice of van der Pol oscillators
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2020-09-08 , DOI: 10.1016/j.cnsns.2020.105513
I.A. Shepelev , V.S. Anishchenko

The present work is devoted to the numerical analysis of the dynamics of a 2D lattice of coupled van der Pol oscillators in the regime of relaxation oscillations. It is shown that the influence of coupling leads to the shift of effective values of the control parameters of individual oscillators. The strong coupling can even cause the transition to bistable dynamics which is never observed in a single van der Pol oscillator. The numerically constructed phase-parametric diagram that takes into account the shifts of parameters shows that the bistability arises through the pitchfork bifurcation when varying the coupling strength. The lattice dynamics is analyzed when the control and coupling parameters are varied within a wide range, and the regime diagrams are constructed in the planes of system parameters. A new type of spatiotemporal pattern, a so-called ”labyrinth-like structure”, is found and described in detail. We also reveal for the first time and study a spiral wave chimera with a new kind of the incoherence core in the form of ”labyrinth-like structure”.



中文翻译:

van der Pol振荡器的二维晶格中的双稳态迷宫状结构和嵌合状态

目前的工作致力于在松弛振荡状态下耦合范德波尔振荡器的二维晶格动力学的数值分析。结果表明,耦合的影响导致各个振荡器控制参数有效值的偏移。强耦合甚至可能导致过渡到双稳态动力学,这在单个van der Pol振荡器中从未观察到。数值计算的相位参数图考虑了参数的变化,表明在改变耦合强度时,通过叉形分叉会产生双稳态。当控制参数和耦合参数在较大范围内变化时,将分析晶格动力学,并在系统参数平面中构造状态图。一种新型的时空模式 找到并详细描述了所谓的“迷宫状结构”。我们还首次揭示并研究了一种以“迷宫状结构”形式出现的新型非相干核的螺旋波嵌合体。

更新日期:2020-09-08
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