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| 2. | Punetha, Nirmal; Ujjwal, Sangeeta Rani; Atay, Fatihcan M; Ramaswamy, Ramakrishna Delay-induced remote synchronization in bipartite networks of phase oscillators Journal Article Physical Review E – Statistical, Nonlinear, and Soft Matter Physics, 91 (2), pp. 1–7, 2015, ISSN: 15502376. Abstract | Links | BibTeX | Tags: Bipartite Network, Delay, Synchronization @article{Punetha2015, title = {Delay-induced remote synchronization in bipartite networks of phase oscillators}, author = {Nirmal Punetha and Sangeeta Rani Ujjwal and Fatihcan M Atay and Ramakrishna Ramaswamy}, url = {https://ramramaswamy.org/papers/159.pdf}, doi = {10.1103/PhysRevE.91.022922}, issn = {15502376}, year = {2015}, date = {2015-01-01}, journal = {Physical Review E – Statistical, Nonlinear, and Soft Matter Physics}, volume = {91}, number = {2}, pages = {1–7}, abstract = {We study a system of mismatched oscillators on a bipartite topology with time-delay coupling, and analyze the synchronized states. For a range of parameters, when all oscillators lock to a common frequency, we find solutions such that systems within a partition are in complete synchrony, while there is lag synchronization between the partitions. Outside this range, such a solution does not exist and instead one observes scenarios of remote synchronization—namely, chimeras and individual synchronization, where either one or both of the partitions are synchronized independently. In the absence of time delay such states are not observed in phase oscillators.}, keywords = {Bipartite Network, Delay, Synchronization}, pubstate = {published}, tppubtype = {article} } We study a system of mismatched oscillators on a bipartite topology with time-delay coupling, and analyze the synchronized states. For a range of parameters, when all oscillators lock to a common frequency, we find solutions such that systems within a partition are in complete synchrony, while there is lag synchronization between the partitions. Outside this range, such a solution does not exist and instead one observes scenarios of remote synchronization—namely, chimeras and individual synchronization, where either one or both of the partitions are synchronized independently. In the absence of time delay such states are not observed in phase oscillators. |
| 1. | Punetha, Nirmal; Ramaswamy, Ramakrishna; Atay, Fatihcan M Bipartite networks of oscillators with distributed delays: Synchronization branches and multistability Journal Article Physical Review E – Statistical, Nonlinear, and Soft Matter Physics, 91 (4), pp. 1–10, 2015, ISSN: 15502376. Abstract | Links | BibTeX | Tags: Bipartite Network, Multistability, Synchronization @article{Punetha2015a, title = {Bipartite networks of oscillators with distributed delays: Synchronization branches and multistability}, author = {Nirmal Punetha and Ramakrishna Ramaswamy and Fatihcan M Atay}, url = {https://ramramaswamy.org/papers/160.pdf}, doi = {10.1103/PhysRevE.91.042906}, issn = {15502376}, year = {2015}, date = {2015-01-01}, journal = {Physical Review E – Statistical, Nonlinear, and Soft Matter Physics}, volume = {91}, number = {4}, pages = {1–10}, abstract = {We study synchronization in bipartite networks of phase oscillators with general nonlinear coupling and distributed time delays. Phase-locked solutions are shown to arise, where the oscillators in each partition are perfectly synchronized among themselves but can have a phase difference with the other partition, with the phase difference necessarily being either zero or $pi$ radians. Analytical conditions for the stability of both types of solutions are obtained and solution branches are explicitly calculated, revealing that the network can have several coexisting stable solutions. With increasing value of the mean delay, the system exhibits hysteresis, phase flips, final state sensitivity, and an extreme form of multistability where the numbers of stable in-phase and antiphase synchronous solutions with distinct frequencies grow without bound. The theory is applied to networks of Landau-Stuart and Rossler oscillators and shown to accurately predict both in-phase and antiphase synchronous behavior in appropriate parameter ranges.}, keywords = {Bipartite Network, Multistability, Synchronization}, pubstate = {published}, tppubtype = {article} } We study synchronization in bipartite networks of phase oscillators with general nonlinear coupling and distributed time delays. Phase-locked solutions are shown to arise, where the oscillators in each partition are perfectly synchronized among themselves but can have a phase difference with the other partition, with the phase difference necessarily being either zero or $pi$ radians. Analytical conditions for the stability of both types of solutions are obtained and solution branches are explicitly calculated, revealing that the network can have several coexisting stable solutions. With increasing value of the mean delay, the system exhibits hysteresis, phase flips, final state sensitivity, and an extreme form of multistability where the numbers of stable in-phase and antiphase synchronous solutions with distinct frequencies grow without bound. The theory is applied to networks of Landau-Stuart and Rossler oscillators and shown to accurately predict both in-phase and antiphase synchronous behavior in appropriate parameter ranges. |