Networks and their generalization: hypergraphs have been a useful tool to model connections in many complex systems. Recently, there has been growing interest on studying dynamical systems on hypergraphs, for their flexibility to incorporate group-wise interactions, which often go missed in traditional networks. Examples of systems with group-wise interactions include coupled oscillators, species interactions in ecosystems, and neuroscience. Existing studies elucidate that network and hypergraph structures can have profound effects on the dynamics of complex systems such as synchronization and contagion processes, consensus formation, percolation, and ecological systems.
This Research Topic focuses on further understanding the effects of the network and hypergraph structures on the dynamics of complex systems such as synchronization processes, consensus formation, ecological systems, random walks, epidemic spreading, and neural dynamics. It aims to discover and highlight novel states that may arise in these dynamical systems due to different network and hypergraph structures and topologies. Authors may consider networks that are time-varying or static or multiplex with different properties such as communities, correlations, different levels of group-wise interactions, and more. For an example, a network of coupled oscillators with community structure result in hierarchical synchronization. Similarly, coupled oscillator systems with community structure, heterogenous coupling strengths, and phase lags give rise to chaos. In the case of contagion and synchronization processes on hypergraphs, there is a prevalence of exciting results such as bistability, abrupt phase transitions, and hysteresis.
This Research Topic seeks research papers that focus on unraveling varied and novel dynamical behaviors of the complex systems mentioned above. The authors may support their results by using numerical simulations and/or developing analytical tools. The goal of this Research Topic is to further our understanding of different dynamical systems that have applications across the fields of applied mathematics, biology, neuroscience, epidemiology, and more.
Topics of interest include, but are not limited to:
· Synchronization of coupled oscillators on hypergraphs with different structures and properties
· Contagion processes on hypergraphs with different structures and properties
· Random walk models on hypergraphs
· Competition dynamics on networks and hypergraphs
· Consensus formation and opinion dynamics on time-varying, static networks, and hypergraphs
· Cascading behavior in networks
Keywords:
Networks, Hypergraphs, Dynamical Systems, Analytical and Numerical Methods, Synchronization Processes
Important Note:
All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.
Networks and their generalization: hypergraphs have been a useful tool to model connections in many complex systems. Recently, there has been growing interest on studying dynamical systems on hypergraphs, for their flexibility to incorporate group-wise interactions, which often go missed in traditional networks. Examples of systems with group-wise interactions include coupled oscillators, species interactions in ecosystems, and neuroscience. Existing studies elucidate that network and hypergraph structures can have profound effects on the dynamics of complex systems such as synchronization and contagion processes, consensus formation, percolation, and ecological systems.
This Research Topic focuses on further understanding the effects of the network and hypergraph structures on the dynamics of complex systems such as synchronization processes, consensus formation, ecological systems, random walks, epidemic spreading, and neural dynamics. It aims to discover and highlight novel states that may arise in these dynamical systems due to different network and hypergraph structures and topologies. Authors may consider networks that are time-varying or static or multiplex with different properties such as communities, correlations, different levels of group-wise interactions, and more. For an example, a network of coupled oscillators with community structure result in hierarchical synchronization. Similarly, coupled oscillator systems with community structure, heterogenous coupling strengths, and phase lags give rise to chaos. In the case of contagion and synchronization processes on hypergraphs, there is a prevalence of exciting results such as bistability, abrupt phase transitions, and hysteresis.
This Research Topic seeks research papers that focus on unraveling varied and novel dynamical behaviors of the complex systems mentioned above. The authors may support their results by using numerical simulations and/or developing analytical tools. The goal of this Research Topic is to further our understanding of different dynamical systems that have applications across the fields of applied mathematics, biology, neuroscience, epidemiology, and more.
Topics of interest include, but are not limited to:
· Synchronization of coupled oscillators on hypergraphs with different structures and properties
· Contagion processes on hypergraphs with different structures and properties
· Random walk models on hypergraphs
· Competition dynamics on networks and hypergraphs
· Consensus formation and opinion dynamics on time-varying, static networks, and hypergraphs
· Cascading behavior in networks
Keywords:
Networks, Hypergraphs, Dynamical Systems, Analytical and Numerical Methods, Synchronization Processes
Important Note:
All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.