Journal of Information Processing Systems

Korea Information Processing Society (한국정보처리학회)
권호 표지
DOI QR코드

DOI QR Code

Formulating Analytical Solution of Network ODE Systems Based on Input Excitations

  • Bagchi, Susmit (Dept. of Aerospace and Software Engineering (Informatics), Gyeongsang National University)
  • Received : 2017.05.24
  • Accepted : 2017.07.05
  • Published : 2018.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

The concepts of graph theory are applied to model and analyze dynamics of computer networks, biochemical networks and, semantics of social networks. The analysis of dynamics of complex networks is important in order to determine the stability and performance of networked systems. The analysis of non-stationary and nonlinear complex networks requires the applications of ordinary differential equations (ODE). However, the process of resolving input excitation to the dynamic non-stationary networks is difficult without involving external functions. This paper proposes an analytical formulation for generating solutions of nonlinear network ODE systems with functional decomposition. Furthermore, the input excitations are analytically resolved in linearized dynamic networks. The stability condition of dynamic networks is determined. The proposed analytical framework is generalized in nature and does not require any domain or range constraints.

Keywords

References

  1. D. Tipper and M. K. Sundareshan, "Numerical methods for modeling computer networks under nonstationary conditions," IEEE Journal on Selected Areas in Communications, vol. 8, no. 9, pp. 1682-1695, 1990. https://doi.org/10.1109/49.62855
  2. M. S. Obaidat, F. Zarai, and P. Nicopolitidis, Modeling and Simulation of Computer Networks and Systems: Methodologies and Applications. Amsterdam: Morgan Kaufmann, 2015.
  3. M. Medykovsky, I. Droniuk, M. Nazarkevich, and O. Fedevych, "Modelling the pertubation of traffic based on ateb-functions," in International Conference on Computer Networks, Lwowek Slaski, Poland, 2013, pp. 38-44.
  4. S. J. Ridden and B. D. MacArthur, "Cell fate regulatory networks," in New Frontiers of Network Analysis in Systems Biology. Dordrecht: Springer, 2012.
  5. C. Stotzel, S. Roblitz, and H. Siebert, "Complementing ODE-based system analysis using Boolean networks derived from an Euler-like transformation," PloS One, vol. 10, article no. e0140954, 2015.
  6. B. Bylina, M. Karwacki, and J. Bylina, "A CPU-GPU hybrid approach to the uniformization method for solving Markovian models: a case study of a wireless network," in Proceedings of the 19th International Conference on Computer Networks, Szczyrk, Poland, 2012, pp. 401-410.
  7. W. A. Massey and W. Whitt, "Networks of infinite-server queues with nonstationary Poisson input," Queueing Systems, vol. 13, no. 1-3, pp. 183-250, 1993. https://doi.org/10.1007/BF01158933
  8. C. Casetti, R. L. Cigno, M. Mellia, M.,Munafo, and Z. Zsoka, "A new class of QoS routing strategies based on network graph reduction," Computer Networks, vol. 41, no. 4, pp. 475-487, 2003. https://doi.org/10.1016/S1389-1286(02)00414-0
  9. M. Herty, A. Klar, and A. K. Singh, "An ODE traffic network model," Journal of Computational and Applied Mathematics, vol. 203, no. 2, pp. 419-436, 2007. https://doi.org/10.1016/j.cam.2006.04.007
  10. D. Minerva, S. Kawasaki, and T. Suzuki, "Pathway network analysis and an application to the ODE model of MMP2 activation in the early stage of cancer cell invasion," AIP Conference Proceedings, vol. 1651, no. 1, pp. 99-104, 2015.
  11. S. Soliman and M. Heiner, "A unique transformation from ordinary differential equations to reaction networks," PloS One, vol. 5, article no. e14284, 2010.
  12. E. Stai, V. Karyotis, and S. Papavassiliou, "Analysis and control of information diffusion dictated by user interest in generalized networks," Computational Social Networks, vol. 2, article no. 18, 2015.
  13. J. Yang and J. Leskovec, "Modeling information diffusion in implicit networks," in Proceedings of the IEEE 10th International Conference on Data Mining, Sydney, Australia, 2010, pp. 599-608.
  14. A. Davoudi and M. Chatterjee, "Prediction of information diffusion in social networks using dynamic carrying capacity," in Proceedings of the IEEE International Conference on Big Data, Washington, DC, 2016, pp. 2466-2469.
  15. M. H. R. Khouzani, S. Sarkar, and E. Altman, "Maximum damage malware attack in mobile wireless networks," IEEE/ACM Transactions on Networking, vol. 20, no. 5, pp. 1347-1360, 2012. https://doi.org/10.1109/TNET.2012.2183642
  16. K. Burrage and B. Pohl, "Implementing an ODE code on distributed memory computers," Computers & Mathematics with Applications, vol. 28, no. 10-12, pp. 235-252, 1994. https://doi.org/10.1016/0898-1221(94)00194-4
  17. I. E. Lagaris, A. Likas, and D. I. Fotiadis, "Artificial neural networks for solving ordinary and partial differential equations," IEEE Transactions on Neural Networks, vol. 9, no. 5, pp. 987-1000, 1998. https://doi.org/10.1109/72.712178
  18. A. J. Meade and A. A. Fernandez, "The numerical solution of linear ordinary differential equations by feedforward neural networks," Mathematical and Computer Modelling, vol. 19, no. 12, pp. 1v25, 1994. https://doi.org/10.1016/0895-7177(94)90061-2
  19. N. Mai-Duy, "Solving high order ordinary differential equations with radial basis function networks," International Journal for Numerical Methods in Engineering, vol. 62, no. 6, pp. 824-852, 2005. https://doi.org/10.1002/nme.1220