Abstract

The aim of the research is to study the influence of inhomogeneity in a control parameter of all partial elements in a ring of nonlocally coupled chaotic maps on the possibility of observing chimera states in the system and to compare the changes in regions of chimera realization using different methods of introducing the inhomogeneity. Methods. In this paper, snapshots of the system dynamics are constructed for various values of the parameters, as well as spatial distributions of cross-correlation coefficient values, which enable us to determine the regime observed in the system for these parameters. To improve the accuracy of the obtained results, the numerical studies are carried out for fifty different realizations of initial conditions of the ring elements. Results. It is shown that a fixed inhomogeneous distribution of the control parameters with increasing noise intensity leads to an increase in the range of the coupling strength where chimera states are observed. With this, the boundary lying in the region of strong coupling changes more significantly as compared with the case of weak coupling strength. The opposite effect is provided when the control parameters are permanently affected by noise. In this case increasing the noise intensity leads to a decrease in the interval of existence of chimera states. Additionally, the nature of the random variable distribution (normal or uniform one) does not strongly influence the observed changes in the ring dynamics. The regions of existence of chimera states are constructed in the plane of «coupling strength – noise intensity» parameters. Conclusion. We have studied how the region of existence of chimeras changes when the coupling strength between the ring elements is varied and when different characteristics of the inhomogeneous distribution of the control parameters are used. It has been shown that in order to increase the region of observing chimera states, the control parameters of the elements must be distributed inhomogeneously over the entire ensemble. To reduce this region, a constant noise effect on the control parameters should be used.

Highlights

  • For citation: Nechaev VA, Rybalova EV, Strelkova GI

  • We have studied how the region of existence of chimeras changes when the coupling strength between the ring elements is varied and when different characteristics of the inhomogeneous distribution of the control parameters are used

  • 9. Semenova N., Zakharova A., Anishchenko V., Scholl E

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Summary

Модель и методы исследования

Исследуемая в работе система представляет собой кольцо одномерных отображений с нелокальной связью и описывается следующим уравнением: i+R xni +1. Данный параметр можно расписать как αni = α0 + Dαξni + +Aαψni , где ξni – генератор шума с равномерным распределением в интервале [−1; 1], Dα – интенсивность равномерно распределенного шума (2Dα – ширина интервала, в котором равномерно распределены случайные значения), ψni – генератор шума со стандартным нормальным распределением (μ = 0, σξ = 1), Aα – интенсивность нормально распределенного шума или стандартное отклонение. В этом случае αi = α0 + Dαξi + Aαψi; 2) случайное распределение параметра меняется в начале каждой итерации, при этом αni = α0 + Dαξni + Aαψni. Большая часть случайной величины с нормальным распределением расположена в интервале [−3A; 3A], поэтому в нашей работе максимум интенсивности нормально распределенного шума выбирался в три раза меньше, чем максимум равномерно распределенного шума (Dmax = 3Amax).

Неоднородное распределение значений управляющего параметра по ансамблю
Постоянное шумовое воздействие на управляющий параметр каждого элемента

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