Vibrational resonance in biological nonlinear maps |
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Authors: | S Rajasekar Javier Used |
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Institution: | a School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamilnadu, India b Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain |
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Abstract: | We investigate vibrational resonance in two different nonlinear maps driven by a biharmonic force: the Bellows and the Rulkov map. These two maps possess dynamical features of particular interest for the study of these phenomena. In both maps, the resonance occurs at the low-frequency of the biharmonic signal as the amplitude of the high-frequency signal is varied. We also consider an array of unidirectionally coupled maps with the forcing signal applied to the first unit. In this case, a signal propagation with several interesting features above a critical value of the coupling strength is found, while the response amplitude of the ith unit is greater than the first one. This response evolves in a sigmoidal fashion with the system number i, meaning that at some point the amplitudes saturate. The unidirectional coupling acts as a low-pass filter for distant units. Moreover, the analysis of the mean residence time of the trajectory in a given region of the phase space unveils a multiresonance mechanism in the coupled map system. These results point at the relevance of the discrete-time models for the study of resonance phenomena, since analyses and simulations are much easier than for continuous-time models. |
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Keywords: | Vibrational resonance Biharmonic force Bellows map Rulkov map Signal propagation |
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