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Recent research on the network modeling of complex systems has led to a convenient representation of numerous natural, social, and engineered systems that are now recognized as networks of interacting parts. Such systems can exhibit a…

Synchronous generators and inverter-based resources are complex systems with dynamics that cut across multiple intertwined physical domains and control loops. Modeling individual generators and inverters is, in itself, a very involved…

The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory--inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in…

Synchronization in networks of oscillatory units is an emergent phenomenon present in various systems, such as biological, technological, and social systems. Many real-world systems have adaptive properties, meaning that their…

Adaptive network dynamical systems describe the co-evolution of dynamical quantities on the nodes as well as dynamics of the network connections themselves. For dense networks of many nodes, the resulting dynamics are typically…

Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's…

Entrainment of randomly coupled oscillator networks by periodic external forcing applied to a subset of elements is numerically and analytically investigated. For a large class of interaction functions, we find that the entrainment window…

Spiking neural networks are nature's versatile solution to fault-tolerant and energy efficient signal processing. To translate these benefits into hardware, a growing number of neuromorphic spiking neural network processors attempt to…

Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…

Drawing inspiration from real world interacting systems we study a system consisting of two networks that exhibit antagonistic and dependent interactions. By antagonistic and dependent interactions, we mean, that a proportion of functional…

We examine the qualitative and quantitative properties of continuous attractor networks in explaining the dynamics of grid cells.

In adaptive dynamical networks, the dynamics of the nodes and the edges influence each other. We show that we can treat such systems as a closed feedback loop between edge and node dynamics. Using recent advances on the stability of…

Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…

The brain rapidly adapts to new contexts and learns from limited data, a coveted characteristic that artificial intelligence (AI) algorithms struggle to mimic. Inspired by the mechanical oscillatory rhythms of neural cells, we developed a…

Synchronized neural spiking is associated with many cognitive functions and thus, merits study for its own sake. The analysis of neural synchronization naturally leads to the study of repetitive spiking and consequently to the analysis of…

This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…

Plasticity, the ability of a neural network to quickly change its predictions in response to new information, is essential for the adaptability and robustness of deep reinforcement learning systems. Deep neural networks are known to lose…

A central question of network science is how functional properties of systems arise from their structure. For networked dynamical systems, structure is typically quantified with network measures. A functional property that is of theoretical…

Biological neural networks are characterized by their high degree of plasticity, a core property that enables the remarkable adaptability of natural organisms. Importantly, this ability affects both the synaptic strength and the topology of…

Balanced neural networks -- in which excitatory and inhibitory inputs compensate each other on average -- give rise to a dynamical phase dominated by fluctuations called asynchronous state, crucial for brain functioning. However, structural…