Resonance induced by a spatially periodic force in the reaction-diffusion system

Abstract

The stimulus-dynamic response is an important topic in physics. In this work, we study the dynamics in the reaction-diffusion system subjected to a weak signal and a spatially periodic force. We find that the response of the system to the weak signal is enhanced largely by the spatially periodic force, which is termed spatially periodic-force-induced resonance. In particular, the response becomes stronger when the spatial frequency is chosen such that the system synchronizes with spatially periodic force. This combinative behavior, i.e., the spatially periodic-force-induced resonance and the spatial-synchronization-enhanced resonance, is of great interest and may shed light on our understanding of the dynamics of nonlinear systems subjected to spatially periodic force in responding to a weak signal.

Effects of square spatial periodic forcing on oscillatory hexagon patterns in coupled reaction–diffusion systems

“…Currently, one of the most essential problems in this context is to study the response behaviours of patterns with respect to an external stimulus. [11][12][13][14][15][16][17][18] The external spatial force provides a powerful way to investigate the wavenumber selection mechanism and the controlling mechanism of spatial structures. 14,15 During the past two decades, studies on the effects of spatially periodic force have concentrated on Turing patterns in reaction diffusion systems that undergo Turing instability.…”

“…Currently, one of the most essential problems in this context is to study the response behaviours of patterns with respect to an external stimulus. 11–18 The external spatial force provides a powerful way to investigate the wave-number selection mechanism and the controlling mechanism of spatial structures. 14,15…”

Weak periodic signal detection by sine-Wiener-noise-induced resonance in the FitzHugh–Nagumo neuron

“…Moreover, electromagnetic radiation can induce model selection and transition of electrical activities in neuron, thereby contributing to transmission of complex signals (Ge et al 2017;Lu et al 2017;Wang et al 2017c;Wu et al 2017;Xu et al 2017). The high-frequency (HF) or spatially periodic force with appropriate strength and frequency may augment signal detection and transmission (Yao et al 2015;Yao and Zhan 2010).…”

Breakup of Spiral Wave and Order-Disorder Spatial Pattern Transition Induced by Spatially Uniform Cross-Correlated Sine-Wiener Noises in a Regular Network of Hodgkin-Huxley Neurons

“…Furthermore, CR is sensitive to the amplitudes and correlation times of CCSW noises [19]. CCSW noises [20] can also greatly enhance weak signal detection and transmission through resonance mechanism like periodic force [21][22][23], time delay [24,25], electromagnetic induction [26][27][28][29][30][31], and sine-Wiener noise [32]. Although some studies on CCSW noises have been achieved, to our best knowledge, the effects of CCSW noises on the spiral wave and pattern dynamics have not been so far reported.…”