Diffusion processes are able to describe many dynamic network phenomena, such as the communication between organisms, opinion diffusion in social networks, or herding behavior. Yet current models are not able to capture different updating protocols between the agents, potential asymmetry in the network updates, and external excitation.
Extending results from spectral graph theory, we characterize diffusion of a continuous property by means of a probabilistic model in terms of network stability, the speed of propagation, and resilience with respect to external disturbances.
The developed probabilistic framework is able to describe diffusion in multi-agent networks and focuses on two update protocols where the total amount of the network property is conserved or variable. We demonstrated the ability to achieve diffusion control using either external excitation or modification of the network structure. The probabilistic framework is currently applied to model sequential decision-making in a networked environment and for the analysis and control of migration within an economic union.
Insect outbreaks can have catastrophic effects on forest health. In addition, these outbreaks can be related to the intensification of forest fires and result in considerable economic losses. There is historical evidence that alterations in precipitation and temperature patterns related to climate change can intensify the occurrence of outbreak events. We aim to develop an analytical model and enhance the understanding of outbreak events on multiple spatial scales, from a single forest to large geographical areas.
Many complex systems exhibit critical transitions where a network moves suddenly from a seemingly stable network state to another state. A spatial, multi-layered network approach is necessary to represent spreading effects on different spatial scales. Building on percolation theory and epidemic models, we develop an analytical model to explain the occurrence of critical transitions, taking into account the interactions between local and regional scales. Our model is validated by means of spatiotemporal defoliation data in northern boreal birch forest due to the presence of geometrid moth.
The proposed framework captures the spread and critical transitions of species in a multi-scale spatial model. The understanding of the triggers of these critical transitions is essential for the design of forest management strategies.
Matthias Wildemeersch is a Belgian citizen, and an IIASA-funded Postdoctoral Scholar (Nov 2014 – Nov 2016).
Last edited: 02 March 2016
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