Abstract and Applied Analysis

Entrained Collective Rhythms of Multicellular Systems: Partial Impulsive Control Strategy

Lifei Chen, Yonghui Sun, and Qingli Yang

Full-text: Open access

Abstract

This paper is concerned with the study of entrained collective rhythms of multicellular systems by using partial impulsive control strategy. The objective is to design an impulsive controller based on only those partially available cell states, so that the entrained collective rhythms are guaranteed for the multicellular systems with cell-to-cell communication mechanism. By using the newly developed impulsive integrodifferential inequality, the sufficient conditions are derived to achieve the entrained collective rhythms of multicellular systems. A synthetic multicellular system with simulation results is finally given to illustrate the usefulness of the developed results.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 175068, 10 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449801

Digital Object Identifier
doi:10.1155/2013/175068

Mathematical Reviews number (MathSciNet)
MR3139469

Zentralblatt MATH identifier
1293.93043

Citation

Chen, Lifei; Sun, Yonghui; Yang, Qingli. Entrained Collective Rhythms of Multicellular Systems: Partial Impulsive Control Strategy. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 175068, 10 pages. doi:10.1155/2013/175068. https://projecteuclid.org/euclid.aaa/1393449801


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References

  • L. Glass, “Synchronization and rhythmic processes in physiology,” Nature, vol. 410, no. 6825, pp. 277–284, 2001.
  • J. Garcia-Ojalvo, M. B. Elowitz, and S. H. Strogatz, “Modeling a synthetic multicellular clock: repressilators coupled by quorum sensing,” Proceedings of the National Academy of Sciences of the United States of America, vol. 101, no. 30, pp. 10955–10960, 2004.
  • D. McMillen, N. Kopell, J. Hasty, and J. J. Collins, “Synchronizing genetic relaxation oscillators by intercell signaling,” Proceedings of the National Academy of Sciences of the United States of America, vol. 99, no. 2, pp. 679–684, 2002.
  • T. Zhou, L. Chen, and R. Wang, “A mechanism of synchronization in interacting multi-cell genetic systems,” Physica D, vol. 211, no. 1-2, pp. 107–127, 2005.
  • E. Ullner, A. Koseska, J. Kurths, E. Volkov, H. Kantz, and J. García-Ojalvo, “Multistability of synthetic genetic networks with repressive cell-to-cell communication,” Physical Review E, vol. 78, no. 3, Article ID 031904, 8 pages, 2008.
  • T. Zhou, J. Zhang, Z. Yuan, and L. Chen, “Synchronization of genetic oscillators,” Chaos, vol. 18, no. 3, Article ID 037126, 20 pages, 2008.
  • Y. Sun, G. Feng, and J. Cao, “A new approach to dynamic fuzzy modeling of genetic regulatory networks,” IEEE Transactions on Nanobioscience, vol. 9, no. 4, pp. 263–272, 2010.
  • M. Mormont and F. Lévi, “Circadian-system alterations during cancer processes: a review,” International Journal of Cancer, vol. 70, no. 2, pp. 241–247, 1997.
  • J. Cao and F. Ren, “Exponential stability of discrete-time genetic regulatory networks with delays,” IEEE Transactions on Neural Networks, vol. 19, no. 3, pp. 520–523, 2008.
  • L. Pan and J. Cao, “Anti-periodic solution for delayed cellular neural networks with impulsive effects,” Nonlinear Analysis: Real World Applications, vol. 12, no. 6, pp. 3014–3027, 2011.
  • Y. Sun, G. Feng, and J. Cao, “Robust stochastic stability analysis of genetic regulatory networks with disturbance attenuation,” Neurocomputing, vol. 79, pp. 39–49, 2012.
  • Q. Zhu and J. Cao, “Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 3, pp. 467–479, 2012.
  • S. Yamaguchi, H. Isejima, T. Matsuo et al., “Synchronization of cellular clocks in the suprachiasmatic nucleus,” Science, vol. 302, no. 5649, pp. 1408–1412, 2003.
  • R. Wang and L. Chen, “Synchronizing genetic oscillators by signaling molecules,” Journal of Biological Rhythms, vol. 20, no. 3, pp. 257–269, 2005.
  • C. Li, L. Chen, and K. Aihara, “Synchronization of coupled nonidentical genetic oscillators,” Physical Biology, vol. 3, no. 1, pp. 37–44, 2006.
  • C. Li, L. Chen, and K. Aihara, “Stochastic synchronization of genetic oscillator networks,” BMC Systems Biology, vol. 1, article 6, 2007.
  • J. Qiu and J. Cao, “Global synchronization of delay-coupled genetic oscillators,” Neurocomputing, vol. 72, no. 16–18, pp. 3845–3850, 2009.
  • P. M. Simon, A. M. Habel, J. A. Daubenspeck, and J. C. Leiter, “Vagal feedback in the entrainment of respiration to mechanical ventilation in sleeping humans,” Journal of Applied Physiology, vol. 89, no. 2, pp. 760–769, 2000.
  • A. Wagemakers, J. Buldu, J. Garcia-Ojalvo, and M. Sanjuan, “Synchronization of electronic genetic networks,” Chaos, vol. 16, no. 1, Article ID 013127, 8 pages, 2006.
  • R. Wang, L. Chen, and K. Aihara, “Synchronizing a multicellular system by external input: an artificial control strategy,” Bioinformatics, vol. 22, no. 14, pp. 1775–1781, 2006.
  • T. F. Schultz and S. A. Kay, “Circadian clocks in daily and seasonal control of development,” Science, vol. 301, no. 5631, pp. 326–328, 2003.
  • Y. Li, Z. Liu, J. Zhang, R. Wang, and L. Chen, “Synchronisation mechanisms of circadian rhythms in the suprachiasmatic nucleus,” IET Systems Biology, vol. 3, no. 2, pp. 100–112, 2009.
  • J. Cao and L. Li, “Cluster synchronization in an array of hybrid coupled neural networks with delay,” Neural Networks, vol. 22, no. 4, pp. 335–342, 2009.
  • W. Yu et al., “Local synchronization of a complex network model,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 39, no. 1, pp. 230–241, 2009.
  • J. Lu, D. W. C. Ho, and J. Cao, “A unified synchronization criterion for impulsive dynamical networks,” Automatica, vol. 46, no. 7, pp. 1215–1221, 2010.
  • J. Lu, D. W. C. Ho, J. Cao, and J. Kurths, “Exponential synchronization of linearly coupled neural networks with impulsive disturbances,” IEEE Transactions on Neural Networks, vol. 22, no. 2, pp. 329–335, 2011.
  • X. Yang, J. Cao, and J. Lu, “Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and impulsive control,” IEEE Transactions on Circuits and Systems, vol. 59, no. 2, pp. 371–384, 2012.
  • D. T. Kaplan, J. R. Clay, T. Manning, L. Glass, M. R. Guevara, and A. Shrier, “Subthreshold dynamics in periodically stimulated squid giant axons,” Physical Review Letters, vol. 76, no. 21, pp. 4074–4077, 1996.
  • T. Zhou, J. Zhang, Z. Yuan, and A. Xu, “External stimuli mediate collective rhythms: artificial control strategies,” PLoS ONE, vol. 2, no. 2, article e231, 2007.
  • G. Feng and J. Cao, “Master-slave synchronization of chaotic systems with a modified impulsive controller,” Advances in Difference Equations, vol. 2013, article 24, 2013.
  • X. Yang, J. Cao, and Z. Yang, “Synchronization of coupled reaction-diffusion neural networks with time-varying delays via pinning-impulsive controller,” SIAM Journal on Control and Optimization, vol. 51, no. 5, pp. 3486–3510, 2013.
  • J. Lu, D. W. C. Ho, J. Cao, and J. Kurths, “Single impulsive controller for globally exponential synchronization of dynamical networks,” Nonlinear Analysis: Real World Applications, vol. 14, no. 1, pp. 581–593, 2013.
  • B. C. Goodwin, “Oscillatory behavior in enzymatic control processes,” Advances in Enzyme Regulation, vol. 3, pp. 425–438, 1965.
  • T. S. Gardner, C. R. Cantor, and J. J. Collins, “Construction of a genetic toggle switch in Escherichia coli,” Nature, vol. 403, no. 6767, pp. 339–342, 2000.
  • M. B. Miller and B. L. Bassler, “Quorum sensing in bacteria,” Annual Review of Microbiology, vol. 55, pp. 165–199, 2001.
  • L. Huang, Linear Algebra in Systems and Control Theory, Science Press, Beijing, China, 1984.
  • R. Bellman, “The stability of solutions of linear differential equations,” Duke Mathematical Journal, vol. 10, pp. 643–647, 1943.
  • W. Wang and J. Cao, “Synchronization in an array of linearly coupled networks with time-varying delay,” Physica A, vol. 366, pp. 197–211, 2006.
  • P. Li, J. Cao, and Z. Wang, “Robust impulsive synchronization of coupled delayed neural networks with uncertainties,” Physica A, vol. 373, pp. 261–272, 2007.
  • J. Cao, D. W. C. Ho, and Y. Yang, “Projective synchronization of a class of delayed chaotic systems via impulsive control,” Physics Letters A, vol. 373, no. 35, pp. 3128–3133, 2009.
  • Y. Yang and J. Cao, “Exponential synchronization of the complex dynamical networks with a coupling delay and impulsive effects,” Nonlinear Analysis: Real World Applications, vol. 11, no. 3, pp. 1650–1659, 2010.
  • C. P. Fall, E. S. Marland, J. M. Wagner, and J. J. Tyson, Eds., Computational Cell Biology, vol. 20 of Interdisciplinary Applied Mathematics, Springer, New York, NY, USA, 2005.
  • A.-L. Barabási and R. Albert, “Emergence of scaling in random networks,” Science, vol. 286, no. 5439, pp. 509–512, 1999.