$\require{mediawiki-texvc}$

연합인증

연합인증 가입 기관의 연구자들은 소속기관의 인증정보(ID와 암호)를 이용해 다른 대학, 연구기관, 서비스 공급자의 다양한 온라인 자원과 연구 데이터를 이용할 수 있습니다.

이는 여행자가 자국에서 발행 받은 여권으로 세계 각국을 자유롭게 여행할 수 있는 것과 같습니다.

연합인증으로 이용이 가능한 서비스는 NTIS, DataON, Edison, Kafe, Webinar 등이 있습니다.

한번의 인증절차만으로 연합인증 가입 서비스에 추가 로그인 없이 이용이 가능합니다.

다만, 연합인증을 위해서는 최초 1회만 인증 절차가 필요합니다. (회원이 아닐 경우 회원 가입이 필요합니다.)

연합인증 절차는 다음과 같습니다.

최초이용시에는
ScienceON에 로그인 → 연합인증 서비스 접속 → 로그인 (본인 확인 또는 회원가입) → 서비스 이용

그 이후에는
ScienceON 로그인 → 연합인증 서비스 접속 → 서비스 이용

연합인증을 활용하시면 KISTI가 제공하는 다양한 서비스를 편리하게 이용하실 수 있습니다.

[해외논문] State-Dependent Dynamics of the Lohe Matrix Ensemble on the Unitary Group under the Gradient Flow

SIAM journal on applied dynamical systems, v.19 no.2, 2020년, pp.1080 - 1123  

Kim, Dohyun

Abstract AI-Helper 아이콘AI-Helper

We study the emergent behavior of the matrix ensemble on the unitary group in which a state of each oscillator is influenced by the relative distances. Thus, the coupling strength becomes a time-dependent function and its temporal evolution is determined by a feedback rule incorporating the linear d...

Keyword

참고문헌 (52)

  1. 1.  V. Avalos-Gaytán, J. A. Almendral, I. Leyva, F. Battiston, V. Nicosia, V. Latora, and S. Boccaletti, Emergent explosive synchronization in adaptive complex networks , Phys. Rev. E (3), 97 (2018), 042301. 

  2. 2.  I. Barbǎlat, Syst$\grave{e}$mes d'$\acute{e}$quations diff$\acute{e}$rentielles oscillations non Lin$\acute{e}$aires , Rev. Math. Pures Appl., 4 (1959), pp. 267--270. 

  3. 3.  N. Bellomo and C. Dogbe, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives , SIAM Rev., 53 (2011), pp. 409--463. 

  4. 4.  N. Bellomo and L. Gibelli, Behavioral crowds: Modeling and Monte Carlo simulations toward validation , Comput. & Fluids, 141 (2016), pp. 13--21. 

  5. 5.  R. Berner, J. Fialkowski, D. Kasatkin, V. Nekorkin, S. Yanchuk, and E. Schöll, Hierarchical frequency clusters in adaptive networks of phase oscillators , Chaos, 29 (2019), 103134. 

  6. 6.  J. Bronski, T. Carty, and S. Simpson, A matrix valued Kuramoto model , J. Stat. Phys., 178 (2020), pp. 595--624. 

  7. 7.  J. C. Bronski, Y. He, X. Li, Y. Liu, D. R. Sponseller, and S. Wolbert, The stability of fixed points for a Kuramoto model with Hebbian interactions, Chaos, 27 (2017), 053110. 

  8. 8.  J. Buck and E. Buck, Biology of synchronous flashing of fireflies , Nature, 211 (1966), pp. 562--564. 

  9. 9.  D. Cumin and C. P. Unsworth, Generalizing the Kuramoto model for the study of neuronal synchronization in the brain , Phys. D, 226 (2007), pp. 181--196. 

  10. 10.  T. Danino, O. Mondragon-Palomino, L. Tsimring, and J. Hasty, A synchronized quorum of genetic clocks , Nature, 463 (2010), pp. 326--330. 

  11. 11.  L. DeVille, Synchronization and stability for quantum Kuramoto , J. Stat. Phys., 174 (2019), pp. 160--187. 

  12. 12.  G. B. Ermentrout, An adaptive model for synchrony in the firefly Pteroptyx Malaccae, J. Math. Biol., 29 (1991), pp. 571--585. 

  13. 13.  R. C. Fetecau and W. Sun, First-order aggregation models and zero inertia limits , J. Differential Equations, 259 (2015), pp. 6774--6802. 

  14. 14.  F. Golse and S.-Y. Ha, A mean-field limit of the Lohe matrix model and emergent dynamics , Arch. Ration. Mech. Anal., 234 (2019), pp. 1445--1491. 

  15. 15.  I. Goychuk, J. Casado-Pascual, M. Morillo, J. Lehmann, and P. Hänggi, Quantum stochastic synchronization , Phys. Rev. Lett., 97 (2006), 210601. 

  16. 16.  G. L. Giorgi, F. Galve, G. Manzano, P. Colet, and R. Zambrini, Quantum correlations and mutual synchronization , Phys. Rev. A (3), 85 (2012), 052101. 

  17. 17.  T. Gregor, K. Fujimoto, N. Masaki, and S. Sawai, The onset of collective behavior in social amoebae , Science, 328 (2010), pp. 1021--1025. 

  18. 18.  S.-Y. Ha and D. Kim, Emergent behavior of a second-order Lohe matrix model on the unitary group , J. Stat. Phys., 175 (2019), pp. 904--931. 

  19. 19.  S.-Y. Ha, D. Kim, D. Kim, H. Park, and W. Shim, Emergent dynamics of the Lohe matrix ensemble on a network under time-delayed interactions , J. Math. Phys., 61 (2020), 012702. 

  20. 20.  S.-Y. Ha, D. Kim, J. Lee, and S. E. Noh, Emergence of aggregation in the swarm sphere model with adaptive coupling law , Kinet. Relat. Models, 12 (2019), pp. 411--444. 

  21. 21.  S.-Y. Ha, D. Ko, and S. W. Ryoo, Emergent dynamics of a generalized Lohe model on some class of Lie groups , J. Stat. Phys., 168 (2017), pp. 171--207. 

  22. 22.  S.-Y. Ha, D. Ko, and S. W. Ryoo, On the relaxation dynamics of Lohe oscillators on some Riemannian manifolds , J. Stat. Phys., 172 (2018), pp. 1427--1478. 

  23. 23.  S.-Y.Ha, J. Lee, Z. Li, and J. Park, Emergent dynamics of Kuramoto oscillators with adaptive couplings: Conservation law and fast learning , SIAM J. Appl. Dyn. Syst., 17 (2018), pp. 1560--1588. 

  24. 24.  S.-Y. Ha and S. W. Ryoo, On the emergence and orbital stability of phase-locked states for the Lohe model , J. Stat. Phys., 163 (2016), pp. 411--439. 

  25. 25.  D. O. Hebb, The Organization of Behavior , Wiley, New York, 1949. 

  26. 26.  H. Huh and S.-Y. Ha, Dynamical system approach to synchronization of the coupled Schrödinger-Lohe system , Quart. Appl. Math., 75 (2017), pp. 555--579. 

  27. 27.  H. Huh and D. Kim, Asymptotic Behavior of Gradient Flows on the Unit Sphere with Various Potentials , manuscript. 

  28. 28.  S. M. Hung and S. N. Givigi, A q-learning approach to flocking with UAVs in a stochastic environment , IEEE Trans. Cybern., 47 (2017), pp. 186--197. 

  29. 29.  H. J. Kimble, The quantum internet , Nature, 453 (2008), pp. 1023--1030. 

  30. 30.  A. Klar and R. Wegener, Enskog-like kinetic models for vehicular traffic , J. Stat. Phys., 87 (1997), pp. 91--114. 

  31. 31.  Y. Kuramoto, Chemical Oscillations, Waves and Turbulence , Springer, Berlin, 1984. 

  32. 32.  Y. Kuramoto, Self-Entrainment of a Population of Coupled Non-linear Oscillators , in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Phys. 39, Springer, Berlin, 1975, pp. 420--422. 

  33. 33.  M. A. Lohe, Non-abelian Kuramoto model and synchronization , J. Phys. A, 42 (2009), 395101. 

  34. 34.  M. A. Lohe, Quantum synchronization over quantum networks , J. Phys. A, 43 (2010), 465301. 

  35. 35.  T. E. Lee and H. R. Sadeghpour, Quantum synchronization of quantum Van der Pol oscillators with trapped ions , Phys. Rev. Lett., 111 (2013), 234101. 

  36. 36.  M. Machida, T. Kano, S. Yamada, M. Okumura, T. Imamura, and T. Koyama, Quantum synchronization effects in intrinsic Josephson junctions , Phys. C, 468 (2008), pp. 689--694. 

  37. 37.  A. Mari, A. Farace, N. Didier, V. Giovannetti, and R. Fazio, Measures of quantum synchronization in continuous variable systems , Phys. Rev. Lett., 111 (2013), 103605. 

  38. 38.  P. Nelson, A kinetic model of vehicular traffic and its associated bimodal equilibrium solution , Transp. Theory Statist. Phys., 24 (1995), pp. 383--409. 

  39. 39.  R. K. Niyogi and L. Q. English, Learning-rate-dependent clustering and self-development in a network of coupled phase oscillators , Phys. Rev. E (3), 80 (2009), 066213. 

  40. 40.  L. Papadopoulos, J. Z. Kim, J. Kurths, and D. Bassett, Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators , Chaos, 27 (2017), 073115. 

  41. 41.  L. Perea, P. Elosegui, and G. Gomez, Extension of the Cucker-Smale control law to space flight formations , J. Guid. Control, 32 (2009), pp. 527--537. 

  42. 42.  C. B. Picallo and H. Riecke, Adaptive oscillator networks with conserved overall coupling: Sequential firing and near-synchronized states , Phys. Rev. E (3), 83 (2011), 036206. 

  43. 43.  Q. Ren and J. Zhao, Adaptive coupling and enhanced synchronization in coupled phase oscillators , Phys. Rev. E (3), 76 (2007), 016207. 

  44. 44.  M. Rubenstein, A. Cornejo, and R. Nagapal, Programmable self-assembly in a thousand-robot swarm , Science, 345 (2014), pp. 795--799. 

  45. 45.  P. Seliger, S. C. Young, and L. S. Tsimring, Plasticity and learning in a network of coupled phase oscillators , Phys. Rev. E (3), 65 (2002), 041906. 

  46. 46.  G. Shi, D. Dong, I. R. Petersen, and K. H. Johansson, Reaching a quantum consensus: Master equations that generate symmetrization and synchronization , IEEE Trans. Automat. Control, 61 (2016), pp. 374--387. 

  47. 47.  A. N. Tikhonov, On systems of differential equations containing parameters , Mat. Sb. (N.S.), 27 (1950), pp. 147--156 (in Russian). 

  48. 48.  L. Timms and L. Q. English, Synchronization in phase-coupled Kuramoto oscillator networks with axonal delay and synaptic plasticity , Phys. Rev. E (3), 89 (2014), 032906. 

  49. 49.  V. M. Vinokur, T. I. Baturina, M. V. Fistul, A. Y. Mironov, M. R. Baklanov, and C. Strunk, Superinsulator and quantum synchronization , Nature, 452 (2008), pp. 613--616. 

  50. 50.  S. Walter, A. Nunnenkamp, and C. Bruder, Quantum synchronization of two Van der Pol oscillators , Ann. Phys., 527 (2015), pp. 131--138. 

  51. 51.  O. V. Zhirov and D. L. Shepelyansky, Quantum synchronization , Eur. Phys. J. D, 38 (2006), pp. 375--379. 

  52. 52.  O. V. Zhirov and D. L. Shepelyansky, Quantum synchronization and entanglement of two qubits coupled to a driven dissipative resonator, Phys. Rev. B (3), 80 (2009), 014519. 

LOADING...

활용도 분석정보

상세보기
다운로드
내보내기

활용도 Top5 논문

해당 논문의 주제분야에서 활용도가 높은 상위 5개 콘텐츠를 보여줍니다.
더보기 버튼을 클릭하시면 더 많은 관련자료를 살펴볼 수 있습니다.

관련 콘텐츠

유발과제정보 저작권 관리 안내
섹션별 컨텐츠 바로가기

AI-Helper ※ AI-Helper는 오픈소스 모델을 사용합니다.

AI-Helper 아이콘
AI-Helper
안녕하세요, AI-Helper입니다. 좌측 "선택된 텍스트"에서 텍스트를 선택하여 요약, 번역, 용어설명을 실행하세요.
※ AI-Helper는 부적절한 답변을 할 수 있습니다.

선택된 텍스트

맨위로