Research



(Hover over to see inter-species
collaboration in the Martens lab ... )


Scientific Interests

My main research interest lies in the study of complex nonlinear dynamical systems. Methods I use include:

To study complex behavior, I investigate problems in mathematical biology (evolutionary and ecological models, cancer development, coupled oscillators) and (bio-)physical systems (coupled oscillator systems and networks, fluid dynamics and pattern formation). I am also working on applying concepts from complex systems to applications of physiological/biomedical interest, in particualr the dynamical behavior of vascular networks and neural networks.


Overview


Network Dynamics in Biology and Technology

[PRESS TO UNFOLD] Network dynamics in vascular physiology



Dynamical Systems Theory

[PRESS TO UNFOLD] Early warning signs of critical transitions in high dimensional systems



Synchronization Dynamics in Biology and Mechanics

[PRESS TO UNFOLD] Synchronization patterns in complex networks


[PRESS TO UNFOLD] Synchronization Theory in Coupled Networks and Nonlinear Dynamics


[PRESS TO UNFOLD] Applying and controlling chimera states in technological and biological settings



Evolutionary and Ecological Dynamics

[PRESS TO UNFOLD] Population dynamics in ecology: Seasonal forcing of trophic chains.


[PRESS TO UNFOLD] Size, sense and allometry of marine life and animals.


[PRESS TO UNFOLD] Population Dynamics in Evolution of Species in Spatially Extended Habitats


[PRESS TO UNFOLD] Cancer progression in spatially extended epithelia



Fluid Instabilities

[PRESS TO UNFOLD] Symmetry breaking and pattern formation in open surface flows



2010 Erik (technique by Sven)