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Heterogeneous networks play a key role in the evolution of communities and the decisions individuals make. These networks link different types of entities, for example, people and the events they attend. Network analysis algorithms usually…
Signal duration (e.g. the time scales over which an active signaling intermediate persists) is a key regulator of biological decisions in myriad contexts such as cell growth, proliferation, and developmental lineage commitments.…
The paradigm of layered networks is used to describe many real-world systems -- from biological networks, to social organizations and transportation systems. Recently there has been much progress in understanding the general properties of…
The state of structural balance (termed also `Heider balance') of a social network is often discussed in social psychology and sociophysics. In this state, actors at network nodes classify other individuals as enemies or friends. Hence, the…
The paper proposes two dynamical systems based on the generalized Lotka-Volterra model of three excitable elements interacting through excitatory couplings. It is shown that for some values of the coupling parameters in the phase space of…
In complex ecosystems such as microbial communities, there is constant ecological and evolutionary feedback between the residing species and the environment occurring on concurrent timescales. Species respond and adapt to their surroundings…
We introduce a multitype contact process with temporal heterogeneity involving two species competing for space on the $d$-dimensional integer lattice. Time is divided into seasons called alternately season 1 and season 2. We prove that…
Neural systems show a modular and typically also a hierarchical organisation across different levels and across different species. Topology relates to function, but it is also influences dynamics as earlier studies showed its effect on…
Ecological models traditionally explain stability and coexistence through pairwise interactions among species. These interactions can also involve groups of three or more species, higher-order interactions, which recent theory suggests can…
This paper considers the evolution of a network in a discrete time, stochastic setting in which agents learn about each other through repeated interactions and maintain/break links on the basis of what they learn from these interactions.…
Coherence evolution of two food web models can be obtained under the stirring effect of chaotic advection. Each food web model sustains a three--level trophic system composed of interacting predators, consumers and vegetation. These…
Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic…
This work studies how to preemptively increase the resilience of a network by means of time-varying topological actuation. To do this, we focus on linear dynamical systems that are compatible with a given network, and consider policies that…
Differential equation-based physiological models of sleep-wake networks describe sleep-wake regulation by simulating the activity of wake- and sleep-promoting neuronal populations and the modulation of these populations by homeostatic and…
Using a vector field in $\mathbb{R}^4$, we provide an example of a robust heteroclinic cycle between two equilibria that displays a mix of features exhibited by well-known types of low-dimensional heteroclinic structures, including simple,…
We study the temporal co-variation of network co-evolution via the cross-link structure of networks, for which we take advantage of the formalism of hypergraphs to map cross-link structures back to network nodes. We investigate two sets of…
We give a constructive method for realizing an arbitrary directed graph (with no one-cycles) as a heteroclinic or an excitable dynamic network in the phase space of a system of coupled cells of two types. In each case, the system is…
Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing…
The asymmetric Hopfield model is used to simulate signaling dynamics in gene/transcription factor networks. The model allows for a direct mapping of a gene expression pattern into attractor states. We analyze different control strategies…
The two most fundamental processes describing change in biology, development and evolu-tion, occur over drastically different timescales, difficult to reconcile within a unified framework. Development involves temporal sequences of cell…