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


Chimera state in mechanical oscillators



The movie shows two coupled populations of metronomes (mechanical pendula) coupled to each other and demonstrating an asymmetric synchronization pattern. Three subsequent time points of the pendulum bob are shown in three different colors. More details here -- http://www.pnas.org/content/110/26/10563

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)