Bulletin of the American Physical Society
2018 Annual Meeting of the APS Mid-Atlantic Section
Volume 63, Number 20
Friday–Sunday, November 9–11, 2018; College Park, Maryland
Session D02: Nonlinear Dynamics |
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Chair: Pratyush Tiwary, University of Maryland, College Park Room: Edward St. John 2212 |
Saturday, November 10, 2018 9:30AM - 10:06AM |
D02.00001: Criticality and Robustness in Networks of Neurons Invited Speaker: Michelle Girvan Experimental evidence suggests that networks of neurons operate near a critical point, i.e., the boundary between an order-disorder phase transition. Criticality provides the order needed for coherent function while at the same time allowing the system the flexibility that is associated with the disordered state. Mathematical models of phase transitions in neuronal networks help us to identify features of the brain's wiring that are key for optimal information processing. |
Saturday, November 10, 2018 10:06AM - 10:42AM |
D02.00002: How to Synchronize Chaotic Systems Invited Speaker: Louis Michael Pecora The concept of synchronized systems has been around for centuries with one of the earliest studies being on the synchronization of clocks by Christiaan Huygens in the mid 1700's. By the mid 1900's it was well-known how to mathematically model the synchronization of systems that oscillated periodically or regularly, i.e. in a steady, repeatable way. But as a new type of motion called chaos started to be studied in the 1970's the notion of synchronization of such systems was difficult to grasp since chaotic systems never repeated or had regular periodic motion. Their movement was complex on all levels and fractal in nature. I'll introduce the notion of chaos and then show how one can synchronize chaotic systems. I'll give a little history of the subject and mention some possible uses proposed for such systems. Although I will start with two synchronized chaotic systems, I'll show how to synchronize an entire network of chaotic oscillators and, more importantly, how to determine the stability of such systems in a way that solves the problem for all networks linking a particular oscillator type at each network node. I'll wind up introducing the more complex problem of cluster synchronization, which is a complicated problem involving a vast number of symmetries. |
Saturday, November 10, 2018 10:42AM - 11:18AM |
D02.00003: Studies of 1D and 2D Chimera States in Populations of Coupled Chemical Oscillators Invited Speaker: Kenneth Showalter We have studied chimera and chimera-like states in populations of photochemically coupled Belousov-Zhabotinsky (BZ) oscillators. Simple chimeras and chimera states with multiple and traveling phase clusters, phase-slip behavior, and chimera-like states with phase waves are described. Simulations with a realistic model of the discrete BZ system of populations of homogeneous and heterogeneous oscillators are compared with each other and with experimental behavior. Spiral wave chimeras as well as chimera core instabilities are studied in large arrays of photochemically coupled oscillators. References: M. R. Tinsley et al., Nature Physics 8, 662 (2012); S. Nkomo et al., Phys. Rev. Lett. 110, 244102 (2013); S. Nkomo et al., Chaos 26, 094826 (2016); J. F. Totz et al., Nature Physics 14, 282 (2018). |
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