Bistability promotes solitary states in ensembles of nonlocally coupled maps

Elena V. Rybalova; Galina I. Strelkova; Tatyana E. Vadivasova; Vadim S. Anishchenko

doi:10.1117/12.2523278

3 June 2019 Bistability promotes solitary states in ensembles of nonlocally coupled maps

Elena V. Rybalova, Galina I. Strelkova, Tatyana E. Vadivasova, Vadim S. Anishchenko

Proceedings Volume 11067, Saratov Fall Meeting 2018: Computations and Data Analysis: from Nanoscale Tools to Brain Functions; 110670P (2019) https://doi.org/10.1117/12.2523278
Event: International Symposium on Optics and Biophotonics VI: Saratov Fall Meeting 2018, 2018, Saratov, Russian Federation

Abstract

In this paper we study numerically a general mechanism of realizing solitary state modes by analyzing the dynamics of one-dimensional ensembles of nonlocally coupled Henon and Lozi maps. It is shown that the main reason of appearing the solitary state regimes consists in the emergence of bistability in individual oscillators of the ensemble. The bistability can arise due to the nonlocal coupling between the ensemble elements, which plays the role of an external force. The numerical findings are illustrated by the construction of basins of attraction of the emerging attractors and their phase portraits in the bistability regime of ensemble elements.

Citation Download Citation

Elena V. Rybalova, Galina I. Strelkova, Tatyana E. Vadivasova, and Vadim S. Anishchenko "Bistability promotes solitary states in ensembles of nonlocally coupled maps", Proc. SPIE 11067, Saratov Fall Meeting 2018: Computations and Data Analysis: from Nanoscale Tools to Brain Functions, 110670P (3 June 2019); https://doi.org/10.1117/12.2523278

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