# Guillermo Espinoza

### From Santa Fe Institute Events Wiki

Hello people

I am currently writing my Ph.D. thesis in Applied Mathematics between University of Chili (Chile) and University of Nice Sophia-Antipolis (France).

### Researh Interests

My Research Interests are Dynamical Systems, Systems Biology, Bifurcation & Chaos, Regulatory Networks and Computational Complexity.

Specifically I have been working in my PhD thesis in four problems:

- The study of circuits in boolean regulatory networks and the Thomas

conjecture between dynamic and topological graph structures. I

- A mathematical model for metal stress response in Halobacterium where

we have constructed a model using differential equations and power law formalism, and we have proved that the system is near to be monotone and presents homeostasis behavior.

- I have studied stochastic modeling and simulations

of quorum sensing or cellular communication problem in P. aeruginosa, working in the stochastic simulation algorithm proposed by Gillespie with fast and slow variables.

- Finally I have worked in the desynchronization of stables systems, using homoclinic orbits, particularly in

applications to the Goodwin model involved in the circadian rhythm, moreover we have designed a program and we have proved stability conditions of the Silnikov type.

### Information

My papers and practical information can be found in my webpage

http://www-math.unice.fr/~gespinoz/

I hope to see you soon in Bariloche