Various synchronous states due to coupling strength inhomogeneity and coupling functions in systems of coupled identical oscillators

The brainstem connectome database

Connectivity data of the nervous system and subdivisions, such as the brainstem, cerebral cortex and subcortical nuclei, are necessary to understand connectional structures, predict effects of connectional disorders and simulate network dynamics. For that purpose, a database was built and analyzed which comprises all known directed and weighted connections within the rat brainstem. A longterm metastudy of original research publications describing tract tracing results form the foundation of the brainstem connectome (BC) database which can be analyzed directly in the framework neuroVIISAS. The BC database can be accessed directly by connectivity tables, a web-based tool and the framework. Analysis of global and local network properties, a motif analysis, and a community analysis of the brainstem connectome provides insight into its network organization. For example, we found that BC is a scale-free network with a small-world connectivity. The Louvain modularity and weighted stochastic block matching resulted in partially matching of functions and connectivity. BC modeling was performed to demonstrate signal propagation through the somatosensory pathway which is affected in Multiple sclerosis.

Measurement(s)	brainstem
Technology Type(s)	tract tracing metastudy
Factor Type(s)	brain region
Sample Characteristic - Organism	Rattus rattus
Sample Characteristic - Environment	Experimental setup
Sample Characteristic - Location	Germany

Phase and amplitude dynamics of coupled oscillator systems on complex networks

We investigated locking behaviors of coupled limit-cycle oscillators with phase and amplitude dynamics. We focused on how the dynamics are affected by inhomogeneous coupling strength and by angular and radial shifts in coupling functions. We performed mean-field analyses of oscillator systems with inhomogeneous coupling strength, testing Gaussian, power-law, and brain-like degree distributions. Even for oscillators with identical intrinsic frequencies and intrinsic amplitudes, we found that the coupling strength distribution and the coupling function generated a wide repertoire of phase and amplitude dynamics. These included fully and partially locked states in which high-degree or low-degree nodes would phase-lead the network. The mean-field analytical findings were confirmed via numerical simulations. The results suggest that, in oscillator systems in which individual nodes can independently vary their amplitude over time, qualitatively different dynamics can be produced via shifts in the coupling strength distribution and the coupling form. Of particular relevance to information flows in oscillator networks, changes in the non-specific drive to individual nodes can make high-degree nodes phase-lag or phase-lead the rest of the network.

Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences

Dynamical systems are widespread, with examples in physics, chemistry, biology, population dynamics, communications, climatology and social science. They are rarely isolated but generally interact with each other. These interactions can be characterized by coupling functions-which contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how each interaction occurs. Coupling functions can be used, not only to understand, but also to control and predict the outcome of the interactions. This theme issue assembles ground-breaking work on coupling functions by leading scientists. After overviewing the field and describing recent advances in the theory, it discusses novel methods for the detection and reconstruction of coupling functions from measured data. It then presents applications in chemistry, neuroscience, cardio-respiratory physiology, climate, electrical engineering and social science. Taken together, the collection summarizes earlier work on coupling functions, reviews recent developments, presents the state of the art, and looks forward to guide the future evolution of the field. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Emergence of oscillatory coexistence with exponentially decayed waiting times in a coupled cyclic competition system

Interpatch migration between two environments is generally considered as a spatial concept and can affect species biodiversity in each patch by inducing flux of population such as inflow and outflow quantities of species. In this paper, we explore the effect of interpatch migration, which can be generally considered as a spatial concept and may affect species biodiversity between two different patches in the perspective of the macroscopic level by exploiting the coupling of two systems, where each patch is occupied by cyclically competing three species who can stably coexist by exhibiting periodic orbits. For two simple scenarios of interpatch migration either single or all species migration, we found that two systems with independently stable coexisting species in each patch are eventually synchronized, and oscillatory behaviors of species densities in two patches become identical, i.e., the synchronized coexistence emerges. In addition, we find that, whether single or all species interpatch migration occurs, the waiting time for the synchronization is exponentially decreasing as the coupling strength is intensified. Our findings suggest that the synchronized behavior of species as a result of migration between different patches can be easily predicted by the coupling of systems and additional information such as waiting times and sensitivity of initial densities.