Chimera states in hybrid coupled neuron populations

Abstract

Here we study the emergence of chimera states, a recently reported phenomenon referring to the coexistence of synchronized and unsynchronized dynamical units, in a population of Morris-Lecar neurons which are coupled by both electrical and chemical synapses, constituting a hybrid synaptic architecture, as in actual brain connectivity. This scheme consists of a nonlocal network where the nearest neighbor neurons are coupled by electrical synapses, while the synapses from more distant neurons are of the chemical type. We demonstrate that peculiar dynamical behaviors, including chimera state and traveling wave, exist in such a hybrid coupled neural system, and analyze how the relative abundance of chemical and electrical synapses affects the features of chimera and different synchrony states (i.e. incoherent, traveling wave and coherent) and the regions in the space of relevant parameters for their emergence. Additionally, we show that, when the relative population of chemical synapses increases further, a new intriguing chaotic dynamical behavior appears above the region for chimera states. This is characterized by the coexistence of two distinct synchronized states with different amplitude, and an unsynchronized state, that we denote as a chaotic amplitude chimera. We also discuss about the computational implications of such state.

Physics Clues on the Mind Substrate and Attributes

“…In addition, our mind is so dynamic and adaptive that, not only does it generate new information FIGURE 5 | (Left) Network architecture used for the study of the emergence of chimera behavior using nearest neighbor electrical connections (solid lines) and long-range chemical synapses (dashed lines). (Right) Density plot depicting the time-dependent voltage traces of a 1,000 neuron population interconnected with the topology in the left panel (Calim et al, 2020). This shows the emergence of two chimeras separating different neuron subpopulations with different dynamical regimes, one (the center of the image) with high-amplitude normal spiking activity and the others (the non-centered regions) with high-voltage low amplitude oscillations, constituting a so-called chaotic amplitude chimera (Calim et al, 2020).…”

“…(Right) Density plot depicting the time-dependent voltage traces of a 1,000 neuron population interconnected with the topology in the left panel (Calim et al, 2020). This shows the emergence of two chimeras separating different neuron subpopulations with different dynamical regimes, one (the center of the image) with high-amplitude normal spiking activity and the others (the non-centered regions) with high-voltage low amplitude oscillations, constituting a so-called chaotic amplitude chimera (Calim et al, 2020). Voltage membrane dynamics of the neurons (purple circles in the right panel) has been computed using a Morris-Lecar neuron model (Morris and Lecar, 1981).…”

“…Concerning mind phases, it was just shown (Calim et al, 2020) emergence of chimera states, namely, oscillatory phases where some neurons of the population are coherently oscillating in synchrony and the rest are oscillating out of phase in an asynchronous regime (see Figure 5). This seems robust in many situations, including spiking and bursting neuronal populations and complex network topologies including hybrid synaptic schemes with chemical and electrical connections.…”

What Models and Tools can Contribute to a Better Understanding of Brain Activity?

“…In 2012, and in the years to follow, it was shown that chimeras can be implemented in experimental setups (e.g., Hagerstrom et al, 2012;Tinsley et al, 2012;Totz et al, 2018;Ebrahimzadeh et al, 2020;Gambuzza et al, 2020), providing first evidence that chimera states do not only exist in mathematical models but can also play a role in real-world dynamics. In parallel, various conceptual links were established between chimeras and a variety of natural and man-made networks outside of experimental labs (e.g., Sakaguchi, 2006;Abrams et al, 2008;Ramlow et al, 2019;Calim et al, 2020;Gerster et al, 2020;Rontogiannis and Provata, 2021). Furthermore, approaches to control chimeras were developed (e.g., Sieber et al, 2014;Bick and Martens, 2015;Omelchenko et al, 2018;Ruzzene et al, 2019;Ruzzene et al, 2020;Vadivasova et al, 2020;Zhang and Dai, 2022).…”

“…Therefore, recent work dealt with interactions of chimera states across coupled layers in multilayer networks (e.g., Majhi et al, 2016;Maksimenko et al, 2016;Andrzejak et al, 2017;Andrzejak et al, 2018;Sawicki et al, 2019;Ruzzene et al, 2020;Vadivasova et al, 2020;Rontogiannis and Provata, 2021;Chen et al, 2022). Moreover, various neuron models were used instead of the simple phase oscillators as network nodes (e.g., Sakaguchi, 2006;Hizanidis et al, 2014;Hizanidis et al, 2016;Santos et al, 2017;Chouzouris et al, 2018;Calim et al, 2020;Gerster et al, 2020;Provata and Venetis, 2020;Glaze and Bahar, 2021;Rontogiannis and Provata, 2021;Simo et al, 2021;Zhang and Dai, 2022). In addition, either experimentally obtained real brain connectivity data (e.g., Hizanidis et al, 2016;Santos et al, 2017;Chouzouris et al, 2018;Bansal et al, 2019;Ramlow et al, 2019;Gerster et al, 2020) or basic neuronal connectivity principles (e.g., Rontogiannis and Provata, 2021;Zhang and Dai, 2022) were used to design mathematical model networks capable to show chimera states.…”