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Öbek Eşzamanlılığın Nedensellik Entropisi ile Belirlenmesi

Year 2019, , 1027 - 1036, 20.09.2019
https://doi.org/10.21205/deufmd.2019216330

Abstract

Kaotik sistemler birbirine durum
değişkenleri üzerinden bağlandığında uygun şartlarda öbek eşzamanlılık
gerçekleştirebileceği bilinmektedir. Sürekli zamanlı sistemlerden oluşan böyle
bir ağda örneklenmiş gözlem vektörleri kullanılarak ağın içindeki öbeklerin
belirlenmesi problemi ele alınmıştır. Buna ek olarak; ağ içerisinde bağlantı
şiddetinin değişmesi sonucu yeni öbekler oluşursa öbeklerin yeniden
belirlenebileceği ön görülmektedir. Öbek eşzamanlılığın belirlenmesi için bilgi
kuramı ölçütlerinden biri olan nedensellik entropisi ölçütünün kestirimleri yapılmıştır.
Bu ölçüt aynı ya da farklı öbekte olan kaotik sistemleri birbirinden ayrıştırmaktadır. 

References

  • Strogatz, S. H. 2015. Nonlinear Dynamics and Chaos: with applications to physics, biology, chemistry, and engineering. 2nd edition. CRC Press, 532 s. DOI: 10.1201/9780429492563
  • Pecora L. M., Carroll T. L. 1990. Synchronization in chaotic systems Phys. Rev. Lett., Cilt. 64 (8), s. 821–824. DOI: 10.1103/PhysRevLett.64.821
  • Pecora, L. M., Carroll, T. L., Johnson, G. A., Mar, D. J., Heagy, J. F. 1997. Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos: An Interdisciplinary Journal of Nonlinear Science, Cilt. 7(4), s. 520-543. DOI: 10.1063/1.166278
  • Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L., Zhou, C. S. 2002. The synchronization of chaotic systems. Physics reports, Cilt. 366(1-2), s. 1-101. DOI: 10.1016/S0370-1573(02)00137-0
  • Hasler, M. 1995. Engineering chaos for encryption and broadband communication. Phil. Trans. R. Soc. Lond. A, Cilt. 353(1701), s. 115-126. DOI:10.1098/rsta.1995.0094
  • Li, C., Chen, L., Aihara, K. 2007. Stochastic synchronization of genetic oscillator networks. BMC Systems Biology, Cilt. 1(1), s. 1-6. DOI: 10.1186/1752-0509-1-6
  • Rosenblum, M. G., Pikovsky, A. S., Kurths, J. 1996. Phase synchronization of chaotic oscillators. Physical review letters, Cilt. 76(11), s. 1804-1807. DOI: /10.1103/PhysRevLett.76.1804
  • Rosenblum, M. G., Pikovsky, A. S., Kurths, J. 1997. From phase to lag synchronization in coupled chaotic oscillators. Physical Review Letters, Cilt. 78(22), s. 4193-4196. DOI: 10.1103/PhysRevLett.78.4193
  • Hasler, M., Maistrenko, Y., Popovych, O. 1998. Simple example of partial synchronization of chaotic systems. Physical Review E, Cilt. 58(5), s. 6843-6846. DOI: 10.1103/PhysRevE.58.6843
  • Belykh, I., Belykh, V., Nevidin, K., Hasler, M. 2003. Persistent clusters in lattices of coupled nonidentical chaotic systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, Cilt. 13(1), s. 165-178. DOI: 10.1063/1.1514202
  • Pecora, L. M., Sorrentino, F., Hagerstrom, A. M., Murphy, T. E., Roy, R. 2014. Cluster synchronization and isolated desynchronization in complex networks with symmetries.Nature communications, Cilt. 5, s. 1-8. DOI: 10.1038/ncomms5079
  • Sorrentino, F., Pecora, L. M., Hagerstrom, A. M., Murphy, T. E., Roy, R. 2016. Complete characterization of the stability of cluster synchronization in complex dynamical networks. Science advances, Cilt. 2(4), s. 1-8. DOI: 10.1126/sciadv.1501737
  • Qin, J., Ma, Q., Gao, H., Shi, Y., Kang, Y. 2017. On group synchronization for interacting clusters of heterogeneous systems. IEEE transactions on cybernetics, Cilt. 47(12), s. 4122-4133. DOI: 10.1109/TIE.2017.2711573
  • Belykh, V. N., Belykh, I. V., Hasler, M. 2000. Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems. Physical Review E, Cilt. 62(5), s. 6332-6344. DOI: 10.1103/PhysRevE.62.6332
  • Belykh, V. N., Osipov, G. V., Petrov, V. S., Suykens, J. A., Vandewalle, J. 2008. Cluster synchronization in oscillatory networks. Chaos: An Interdisciplinary Journal of Nonlinear Science, Cilt. 18(3), 037106. DOI: 10.1063/1.2956986
  • Belykh, I., Belykh, V., Hasler, M. 2006. Generalized connection graph method for synchronization in asymmetrical networks. Physica D: Nonlinear Phenomena, Cilt. 224(1-2), s. 42-51. DOI: 10.1016/j.physd.2006.09.014
  • Belykh, V. N., Belykh, I. V., Hasler, M., Nevidin, K. V. 2003. Cluster synchronization in three-dimensional lattices of diffusively coupled oscillators. International Journal of Bifurcation and Chaos, Cilt. 13(04), s. 755-779. DOI: 10.1142/S0218127403006923
  • Ma, Z., Liu, Z., Zhang, G. 2006. A new method to realize cluster synchronization in connected chaotic networks. Chaos: An Interdisciplinary Journal of Nonlinear Science, Cilt. 16(2), 023103. DOI: 10.1063/1.2184948
  • Lu, W., Liu, B., Chen, T. 2010. Cluster synchronization in networks of coupled nonidentical dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, Cilt. 20(1), 013120. DOI:10.1063/1.3329367
  • Kreuz, T., Mormann, F., Andrzejak, R. G., Kraskov, A., Lehnertz, K., Grassberger, P. (2007). Measuring synchronization in coupled model systems: A comparison of different approaches. Physica D: Nonlinear Phenomena, Cilt. 225(1), s. 29-42. DOI: 10.1016/j.physd.2006.09.039
  • Paluš, M., Komárek, V., Hrnčíř, Z., Štěrbová, K. 2001. Synchronization as adjustment of information rates: detection from bivariate time series. Physical Review E, Cilt. 63(4), 046211. DOI: 10.1103/PhysRevE.63.046211
  • Bollt, E. M. 2012. Synchronization as a process of sharing and transferring information. International Journal of Bifurcation and Chaos, Cilt. 22(11), 1250261. DOI: 10.1142/S0218127412502616
  • Sun, J., Bollt, E. M. (2014). Causation entropy identifies indirect influences, dominance of neighbors and anticipatory couplings. Physica D: Nonlinear Phenomena, Cilt. 267, s. 49-57. DOI: 10.1016/j.physd.2013.07.001
  • Singh, H., Misra, N., Hnizdo, V., Fedorowicz, A., Demchuk, E. 2003. Nearest neighbor estimates of entropy. American journal of mathematical and management sciences, Cilt. 23(3-4), s. 301-321. DOI: 10.1080/01966324.2003.10737616
  • Takens, F. 1981. Detecting strange attractors in turbulence. ss 366-381. Dynamical systems and turbulence, Warwick 1980. Springer, Berlin, Heidelberg.
  • Shilnikov, L. P. (2001). Methods of qualitative theory in nonlinear dynamics Cilt. 5, s. 403, World Scientific. DOI: 10.1142/4221
  • Belykh, I., Hasler, M., Lauret, M., Nijmeijer, H., 2005. Synchronization and graph topology. International Journal of Bifurcation and Chaos, Cilt. 15(11), s. 3423-3433. DOI: 10.1142/S0218127405014143
  • Belykh, V. N., Belykh, I. V., Hasler, M., 2004. Connection graph stability method for synchronized coupled chaotic systems. Physica D: nonlinear phenomena, Cilt. 195(1-2), s. 159-187. DOI: 10.1016/j.physd.2004.03.012
  • Strogatz, S. H. 2001. Exploring complex networks. Nature, Cilt. 410(6825), s. 268-276. DOI: 10.1038/35065725
  • Abarbanel, H. 2012. Analysis of observed chaotic data. Springer Science and Business Media. 272 s.
  • Cover, T. M., & Thomas, J. A., 2012. Elements of information theory. John Wiley & Sons. 2nd edition, 748 s.
  • Kraskov, A., Stögbauer, H., Grassberger, P. (2004). Estimating mutual information. Physical review E, Cilt. 69(6), 066138. DOI: 10.1103/PhysRevE.69.066138
  • Zhu, J., Bellanger, J. J., Shu, H., Le Bouquin Jeannès, R. 2015. Contribution to transfer entropy estimation via the k-nearest-neighbors approach. Entropy, Cilt. 17(6), s. 4173-4201. DOI: 10.3390/e17064173
  • Lorenz, E. N., 1963. Deterministic nonperiodic flow. Journal of the atmospheric sciences, Cilt. 20(2), s. 130-141. DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2

Detection of Cluster Synchronization via Causation Entropy

Year 2019, , 1027 - 1036, 20.09.2019
https://doi.org/10.21205/deufmd.2019216330

Abstract

When
chaotic systems are coupled to each other through state variables, the cluster
synchronization can occur in the proper circumstances. The problem of detection
of cluster synchronization by using observation samples has been investigated
in a coupled continuous time chaotic network. If the coupling strengths of this
network change, the network can form new clusters. The detection of clusters
has been also determined in case of rearranging clusters. In order to detect
cluster synchronization,  the causation
entropy has been estimated from observation vectors. This measure has been
shown to distinguish the systems forming in the network. 

References

  • Strogatz, S. H. 2015. Nonlinear Dynamics and Chaos: with applications to physics, biology, chemistry, and engineering. 2nd edition. CRC Press, 532 s. DOI: 10.1201/9780429492563
  • Pecora L. M., Carroll T. L. 1990. Synchronization in chaotic systems Phys. Rev. Lett., Cilt. 64 (8), s. 821–824. DOI: 10.1103/PhysRevLett.64.821
  • Pecora, L. M., Carroll, T. L., Johnson, G. A., Mar, D. J., Heagy, J. F. 1997. Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos: An Interdisciplinary Journal of Nonlinear Science, Cilt. 7(4), s. 520-543. DOI: 10.1063/1.166278
  • Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L., Zhou, C. S. 2002. The synchronization of chaotic systems. Physics reports, Cilt. 366(1-2), s. 1-101. DOI: 10.1016/S0370-1573(02)00137-0
  • Hasler, M. 1995. Engineering chaos for encryption and broadband communication. Phil. Trans. R. Soc. Lond. A, Cilt. 353(1701), s. 115-126. DOI:10.1098/rsta.1995.0094
  • Li, C., Chen, L., Aihara, K. 2007. Stochastic synchronization of genetic oscillator networks. BMC Systems Biology, Cilt. 1(1), s. 1-6. DOI: 10.1186/1752-0509-1-6
  • Rosenblum, M. G., Pikovsky, A. S., Kurths, J. 1996. Phase synchronization of chaotic oscillators. Physical review letters, Cilt. 76(11), s. 1804-1807. DOI: /10.1103/PhysRevLett.76.1804
  • Rosenblum, M. G., Pikovsky, A. S., Kurths, J. 1997. From phase to lag synchronization in coupled chaotic oscillators. Physical Review Letters, Cilt. 78(22), s. 4193-4196. DOI: 10.1103/PhysRevLett.78.4193
  • Hasler, M., Maistrenko, Y., Popovych, O. 1998. Simple example of partial synchronization of chaotic systems. Physical Review E, Cilt. 58(5), s. 6843-6846. DOI: 10.1103/PhysRevE.58.6843
  • Belykh, I., Belykh, V., Nevidin, K., Hasler, M. 2003. Persistent clusters in lattices of coupled nonidentical chaotic systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, Cilt. 13(1), s. 165-178. DOI: 10.1063/1.1514202
  • Pecora, L. M., Sorrentino, F., Hagerstrom, A. M., Murphy, T. E., Roy, R. 2014. Cluster synchronization and isolated desynchronization in complex networks with symmetries.Nature communications, Cilt. 5, s. 1-8. DOI: 10.1038/ncomms5079
  • Sorrentino, F., Pecora, L. M., Hagerstrom, A. M., Murphy, T. E., Roy, R. 2016. Complete characterization of the stability of cluster synchronization in complex dynamical networks. Science advances, Cilt. 2(4), s. 1-8. DOI: 10.1126/sciadv.1501737
  • Qin, J., Ma, Q., Gao, H., Shi, Y., Kang, Y. 2017. On group synchronization for interacting clusters of heterogeneous systems. IEEE transactions on cybernetics, Cilt. 47(12), s. 4122-4133. DOI: 10.1109/TIE.2017.2711573
  • Belykh, V. N., Belykh, I. V., Hasler, M. 2000. Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems. Physical Review E, Cilt. 62(5), s. 6332-6344. DOI: 10.1103/PhysRevE.62.6332
  • Belykh, V. N., Osipov, G. V., Petrov, V. S., Suykens, J. A., Vandewalle, J. 2008. Cluster synchronization in oscillatory networks. Chaos: An Interdisciplinary Journal of Nonlinear Science, Cilt. 18(3), 037106. DOI: 10.1063/1.2956986
  • Belykh, I., Belykh, V., Hasler, M. 2006. Generalized connection graph method for synchronization in asymmetrical networks. Physica D: Nonlinear Phenomena, Cilt. 224(1-2), s. 42-51. DOI: 10.1016/j.physd.2006.09.014
  • Belykh, V. N., Belykh, I. V., Hasler, M., Nevidin, K. V. 2003. Cluster synchronization in three-dimensional lattices of diffusively coupled oscillators. International Journal of Bifurcation and Chaos, Cilt. 13(04), s. 755-779. DOI: 10.1142/S0218127403006923
  • Ma, Z., Liu, Z., Zhang, G. 2006. A new method to realize cluster synchronization in connected chaotic networks. Chaos: An Interdisciplinary Journal of Nonlinear Science, Cilt. 16(2), 023103. DOI: 10.1063/1.2184948
  • Lu, W., Liu, B., Chen, T. 2010. Cluster synchronization in networks of coupled nonidentical dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, Cilt. 20(1), 013120. DOI:10.1063/1.3329367
  • Kreuz, T., Mormann, F., Andrzejak, R. G., Kraskov, A., Lehnertz, K., Grassberger, P. (2007). Measuring synchronization in coupled model systems: A comparison of different approaches. Physica D: Nonlinear Phenomena, Cilt. 225(1), s. 29-42. DOI: 10.1016/j.physd.2006.09.039
  • Paluš, M., Komárek, V., Hrnčíř, Z., Štěrbová, K. 2001. Synchronization as adjustment of information rates: detection from bivariate time series. Physical Review E, Cilt. 63(4), 046211. DOI: 10.1103/PhysRevE.63.046211
  • Bollt, E. M. 2012. Synchronization as a process of sharing and transferring information. International Journal of Bifurcation and Chaos, Cilt. 22(11), 1250261. DOI: 10.1142/S0218127412502616
  • Sun, J., Bollt, E. M. (2014). Causation entropy identifies indirect influences, dominance of neighbors and anticipatory couplings. Physica D: Nonlinear Phenomena, Cilt. 267, s. 49-57. DOI: 10.1016/j.physd.2013.07.001
  • Singh, H., Misra, N., Hnizdo, V., Fedorowicz, A., Demchuk, E. 2003. Nearest neighbor estimates of entropy. American journal of mathematical and management sciences, Cilt. 23(3-4), s. 301-321. DOI: 10.1080/01966324.2003.10737616
  • Takens, F. 1981. Detecting strange attractors in turbulence. ss 366-381. Dynamical systems and turbulence, Warwick 1980. Springer, Berlin, Heidelberg.
  • Shilnikov, L. P. (2001). Methods of qualitative theory in nonlinear dynamics Cilt. 5, s. 403, World Scientific. DOI: 10.1142/4221
  • Belykh, I., Hasler, M., Lauret, M., Nijmeijer, H., 2005. Synchronization and graph topology. International Journal of Bifurcation and Chaos, Cilt. 15(11), s. 3423-3433. DOI: 10.1142/S0218127405014143
  • Belykh, V. N., Belykh, I. V., Hasler, M., 2004. Connection graph stability method for synchronized coupled chaotic systems. Physica D: nonlinear phenomena, Cilt. 195(1-2), s. 159-187. DOI: 10.1016/j.physd.2004.03.012
  • Strogatz, S. H. 2001. Exploring complex networks. Nature, Cilt. 410(6825), s. 268-276. DOI: 10.1038/35065725
  • Abarbanel, H. 2012. Analysis of observed chaotic data. Springer Science and Business Media. 272 s.
  • Cover, T. M., & Thomas, J. A., 2012. Elements of information theory. John Wiley & Sons. 2nd edition, 748 s.
  • Kraskov, A., Stögbauer, H., Grassberger, P. (2004). Estimating mutual information. Physical review E, Cilt. 69(6), 066138. DOI: 10.1103/PhysRevE.69.066138
  • Zhu, J., Bellanger, J. J., Shu, H., Le Bouquin Jeannès, R. 2015. Contribution to transfer entropy estimation via the k-nearest-neighbors approach. Entropy, Cilt. 17(6), s. 4173-4201. DOI: 10.3390/e17064173
  • Lorenz, E. N., 1963. Deterministic nonperiodic flow. Journal of the atmospheric sciences, Cilt. 20(2), s. 130-141. DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
There are 34 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Özge Canlı 0000-0003-3469-5229

Serkan Günel 0000-0002-2971-4483

Publication Date September 20, 2019
Published in Issue Year 2019

Cite

APA Canlı, Ö., & Günel, S. (2019). Öbek Eşzamanlılığın Nedensellik Entropisi ile Belirlenmesi. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi, 21(63), 1027-1036. https://doi.org/10.21205/deufmd.2019216330
AMA Canlı Ö, Günel S. Öbek Eşzamanlılığın Nedensellik Entropisi ile Belirlenmesi. DEUFMD. September 2019;21(63):1027-1036. doi:10.21205/deufmd.2019216330
Chicago Canlı, Özge, and Serkan Günel. “Öbek Eşzamanlılığın Nedensellik Entropisi Ile Belirlenmesi”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi 21, no. 63 (September 2019): 1027-36. https://doi.org/10.21205/deufmd.2019216330.
EndNote Canlı Ö, Günel S (September 1, 2019) Öbek Eşzamanlılığın Nedensellik Entropisi ile Belirlenmesi. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi 21 63 1027–1036.
IEEE Ö. Canlı and S. Günel, “Öbek Eşzamanlılığın Nedensellik Entropisi ile Belirlenmesi”, DEUFMD, vol. 21, no. 63, pp. 1027–1036, 2019, doi: 10.21205/deufmd.2019216330.
ISNAD Canlı, Özge - Günel, Serkan. “Öbek Eşzamanlılığın Nedensellik Entropisi Ile Belirlenmesi”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi 21/63 (September 2019), 1027-1036. https://doi.org/10.21205/deufmd.2019216330.
JAMA Canlı Ö, Günel S. Öbek Eşzamanlılığın Nedensellik Entropisi ile Belirlenmesi. DEUFMD. 2019;21:1027–1036.
MLA Canlı, Özge and Serkan Günel. “Öbek Eşzamanlılığın Nedensellik Entropisi Ile Belirlenmesi”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen Ve Mühendislik Dergisi, vol. 21, no. 63, 2019, pp. 1027-36, doi:10.21205/deufmd.2019216330.
Vancouver Canlı Ö, Günel S. Öbek Eşzamanlılığın Nedensellik Entropisi ile Belirlenmesi. DEUFMD. 2019;21(63):1027-36.

Dokuz Eylül Üniversitesi, Mühendislik Fakültesi Dekanlığı Tınaztepe Yerleşkesi, Adatepe Mah. Doğuş Cad. No: 207-I / 35390 Buca-İZMİR.