Abstract
Neurons are traditionally grouped in two excitability classes, which correspond to two different responses to external inputs, called phase response curves (PRCs). In this paper we have considered a network of two neural populations with delayed couplings, bound in a negative feedback loop by a positive PRC (type I). Making use of both analytical and numerical techniques, we derived the boundaries of stable incoherence in the continuum limit, studying their dependance on the time delay and the strengths of both interpopulation and intrapopulation couplings. This led us to discover, in a system with stronger delayed external compared to internal couplings, the coexistence of areas of coherence and incoherence, called chimera states, that were robust to noise. On the other hand, in the absence of time delays and with negligible internal couplings, the system portrays a family of neutrally stable periodic orbits, known as ``breathing chimeras.''
Highlights
For the past few decades, models of coupled phase oscillators have proved to be successful to describe the emergence of macroscopic rhythmic patterns in a huge variety of natural and artificial contexts [1]
Neurons are traditionally grouped in two excitability classes, which correspond to two different responses to external inputs, called phase response curves (PRCs)
In this paper we have considered a network of two neural populations with delayed couplings, bound in a negative feedback loop by a positive PRC
Summary
For the past few decades, models of coupled phase oscillators have proved to be successful to describe the emergence of macroscopic rhythmic patterns in a huge variety of natural and artificial contexts [1] In this framework, it is useful to consider the interplay between excitatory and inhibitory (E-I) time-delayed connections, in order to model spatially distributed self-organized systems, such as neuronal networks, that are known to exhibit synchronous behavior. The dynamics of networks of type II neurons has been widely explored in the past, e.g., making use of the Kuramoto model and its many generalizations [25,26,27,28,29,30] In this context, chimera states appear commonly in networks of two subpopulations with nonlocal couplings [31], typically with a large ensemble of oscillators ( they have been observed with as few as two oscillators per group [32]). II E the optimal parameters to display chimera states and the robustness of the system towards noise are evaluated
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
