Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:C1L-D

Session:

Number:610

Modulating the oscillations produced by discrete biological models

Tian Ge,  Wei Lin,  Xiaoying Tian,  

pp.610-613

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.610

PDF download (403.1KB)

Summary:
An analytical approach is developed to modulate either the frequency or the amplitude of an oscillator. We present the strategy in general two-dimensional discrete polynomial systems undergoing the Neimark-Sacker bifurcation imposed by designed linear feedback controls, and apply the method to a model of an ideal storage system and the Chialvo neuronal model. Our method shows potential to understand the mechanism of frequency and amplitude modulations in various biological systems.

References:

[1] L. Ashall, et al., “Pulsatile stimulation determines timing and specificity of NF-κ B-dependent transcription,” Science, vol. 324, pp. 242-246, 2009.

[2] C. Gerard and A. Goldbeter, “Temporal self-organization of the cyclin/Cdk network driving the mammalian cell cycle,” Proc. Natl. Acad. Sci. USA, vol. 106, pp. 21643-21648, 2009.

[3] J. R. Pomerening, S. Y. Kim, and J. E. Ferrell, “Systems-level dissection of the cell-cycle oscillator: bypassing positive feedback produces damped oscillations,” Cell, vol. 122, pp. 565-578, 2005.

[4] L. Cai, et al., “Frequency-modulated nuclear localization bursts coordinate gene regulation,” Nature, vol. 455, pp. 485-490, 2008.

[5] A. B. Tort, et al., “Theta-gamma coupling increases during the learning of item-context associations,” Proc. Natl. Acad. Sci. USA, vol. 105, pp. 20942-20947, 2009.

[6] K. M. Kendrick, et al., “Learning alters theta-nested gamma oscillations in inferotemporal cortex,” Nature Precedings, hdl:10101/npre.2009.3151.1, 2009.

[7] T. Y. Tsai, et al., “Robust, Tunable Biological Oscillations from Interlinked Positive and Negative Feedback Loops,” Science, vol. 321, pp. 126-129, 2008.

[8] A. W. M. Dress and W. Lin., “Dynamics of a discrete-time mode of an ‘ideal-storage’ system describing hetero-catalytic processes on metal surfaces,” International Journal of Bifurcation and Chaos, vol. 21, pp. 1331-1339, 2010.

[9] D.R. Chialvo., “Generic excitable dynamics on a two-dimensional map,” Chaos, Solitons & Fractals, vol. 5, pp. 461-479, 1995.

[10] B. Ibarz, J. M. Casado, and M. A. F. Sanjun, “Map-based models in neuronal dynamics,” Physics Report, vol. 501, pp. 1-74, 2011.