Curriculum Vitae. June, 1998 Graduation in Mathematics (5-years degree), Faculty of Sciences of the University of Lisbon (FCUL)

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1 Curriculum Vitae PERSONAL AND INSTITUTIONAL DATA Name: Jorge das Neves Duarte Institutional address: ISEL Engineering Superior Institute of Lisbon, Department of Mathematics, Rua Conselheiro Emídio Navarro, Lisbon, Portugal QUALIFICATIONS / ACADEMIC DEGREES July, 2006 PhD in Mathematics, defended at University of Évora (UE), with the main supervision of Professor José Sousa Ramos (Instituto Superior Técnico (IST), Technical University of Lisbon (UTL)) July, Master of Science in Applied Mathematics, defended at Instituto Superior Técnico (IST), Technical University of Lisbon (UTL), with the main supervision of Professor José Sousa Ramos (IST) June, 1998 Graduation in Mathematics (5-years degree), Faculty of Sciences of the University of Lisbon (FCUL) Certificates of Language courses English Advanced Level by International House London (London, England). English Mastery Stage by Wall Street Institute School of English (Lisbon, Portugal). PROFESSIONAL CAREER Present positions: Adjunt Professor at the Engineering Superior Institute of Lisbon (ISEL), Department of Mathematics, since December 2003 Researcher of the Centre of Mathematical Analysis, Geometry and Dynamical Systems, Department of Mathematics of the Instituto Superior Técnico Member and one of the founders of the Dynamical Systems and Complexity (DySCo) Group Past positions: Assistant Professor at the Engineering Superior Institute of Lisbon (ISEL), Department of Mathematics, from September 2000 to November 2003 Assistant Professor at the Superior Education School of Leiria (ESEL), from September 1999 to August 2000

2 POSITIONS OF ACADEMIC MANAGEMENT Engineering Superior Institute of Lisbon Since 2010 to Present Member of the Coordinating Council of the Department of Mathematics Since 2003 to Member of the Scientific Council of ISEL Since 2003 to 2009 Member of the Scientific Committee of the Chemical Engineering Department (DEQ) RESEARCH INTERESTS Main area of research: Differential Equations and Dynamical Systems The application of mathematical concepts and methods is considered fundamental in the progress of various areas of knowledge such as engineering, chemistry, physics, economics, biology, among others. The issues raised in these areas are proving to be truly exciting, playing a key role in developing theories and new branches of mathematics itself. A privileged area of mathematics, in terms of its conceptual richness and applicability, is the theory of dynamical systems, both discrete and continuous. The theory of dynamical systems integrates, in a harmonious and indispensable way, three major areas of mathematics: analysis, algebra and geometry. The use of computational techniques is usually identified as a catalyst for the development of nonlinear science, unveiling a structured nature behind the complexity. Exploring common structures in different systems, scientists study in an interdisciplinary way the complexity of nature and society. The scientific interests span several fields of dynamical systems theory applied to biological dynamics, especially in the framework of chaotic systems mainly the study of theoretical models of epidemiology, complex ecosystems, virology and catalytic networks in cooperative systems. MAIN PUBLICATIONS Articles in international journals [13] Sardanyés, J., Duarte, J., Januário, C. and Martins, N. Quantifying chaos for ecological stoichiometry, CHAOS 20, (2010) (also selected to appear on the Virtual Journal of Biological Physics Research (2010)) [12] Jorge Duarte, Cristina Januário, Nuno Martins and Josep Sardanyés, Chaos and crisis in a model of cooperative hunting: a symbolic Dynamics approach, Chaos (2009) [11] Jorge Duarte, Cristina Januário, Nuno Martins, Topological entropy and the controlled effect of glucose in the electrical activity of pancreatic β-cells, Physica D 238 (2009), [10] Cristina Januário, Clara Grácio, Diana A. Mendes and Jorge Duarte, Measuring and controlling the chaotic motion of profits, Internat J Bifur Chaos, Vol 19, No. 11 (2009) [9] Cristina Januário, Clara Grácio and Jorge Duarte, Measuring complexity in a business cycle model of the Kaldor type, Chaos, Solitons & Fratals 42 (2009),

3 [8] Jorge Duarte, Cristina Januário and Nuno Martins, Reciprocal inhibitory coupling: Measure and control of chaos on a biophysically motivated model of bursting, Commun Nonlinear Sci Numer Simulat 14 (2009) [7] Jorge Duarte, Cristina Januário and Nuno Martins, Chaos in ecology: the topological entropy of a tritrophic food chain model, Discrete Dynamics in Nature and Society doi: /2008/ (2008) [6] Jorge Duarte, Cristina Januário and Nuno Martins, Topological invariants in the study of a chaotic food chain system, Chaos (2008) (also selected to appear on the Virtual Journal of Biological Physics Research, Vol. 15, Issue 9 (2008)) [5] Jorge Duarte, Luis Silva and J. Sousa Ramos, Computation of the topological entropy in chaotic biophysical bursting models for excitable cells, Discrete Dynamics in Nature and Society (2006), 1-18 [4] Jorge Duarte, Luis Silva and J. Sousa Ramos, The influence of coupling on chaotic maps modelling bursting cells, Chaos, Solitons & Fratals 28 (2006), [3] Jorge Duarte, Luis Silva and J. Sousa Ramos, Types of bifurcations of FitzHugh-Nagumo maps, Nonlinear Dynamics 44 (2006), [2] Jorge Duarte, J. S. Ramos, Topological invariants in forced piecewise-linear Fitzhugh-Nagumo-like systems, Chaos, Solitons & Fratals 23 (2005), [1] Jorge Duarte, J. S. Ramos, Topological Entropy as a Measure of Chaos in Forced Excitable Systems, Int. J. Pure Appl. Math. 4 (2003), no. 2, Articles in proceedings of international conferences [2] Jorge Duarte, Luís Silva and J. Sousa Ramos, Low-dimensional dynamics of cardiac arrhythmias, Proc. of the ECIT European Conference on Iteration Theory - August 29 September 04, 2004 Batschuns, Austria (2006) [1] Jorge Duarte, Luís Silva and J. Sousa Ramos, Symbolic dynamics in the study of bursting electrical activity, in Difference Equations and Discrete Dynamical Systems, Proc. Of the 9th Int. Conference (University of Southern California), Los Angeles (USA), 2-7 August 2004 (World Scientific, 336pp Pub. Date: October 2005) Thesis Jorge Duarte, Chaotic Behaviour in Physiological Systems, PhD Thesis, UE (2006) Jorge Duarte, Harmonic Solutions and Chaos in the Fitzhugh-Nagumo System Under a Periodic Stimulus, Master of Science Thesis, IST (2001)

4 CONFERENCES [17] RIMM-2010 First International Workshop on The Role and Impact of Mathematics in Medicine Henri Poincaré Institute, Paris, June 10-12, 2010, France [16] Jorge Duarte, Measure and control of transient chaos in a food chain model, The 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Dresden University of Technology, May 25-28, 2010, Dresden, Germany. (With Cristina Januário, Nuno Martins and Josep Sardanyés) [15] Jorge Duarte, Chaos and crises in a model for cooperative hunting, Second International Workshop-School, Chaos and Dynamics in Biological Networks', Ecole thématique du CNRS, The Institut d'etudes Scientifiques de Cargèse Corsica, May 3-8, 2010 France. (With Cristina Januário, Nuno Martins and Josep Sardanyés) [14] Jorge Duarte, A chaos generating mechanism and topological entropy in the study of a chaotic food chain system, BICS Conference Multiply Structured Populations in Biology, 1 3 July 2009, University of Bath, England, U.K. (With Cristina Januário and Nuno Martins) [13] Jorge Duarte, Symbolic dynamics and topological entropy in the study of a chaotic food chain system, invited Seminar at the Barcelona Biomedical Research Park 14 th November, 2008, Barcelona, Spain. (With Cristina Januário and Nuno Martins) [12] Topological entropy and the controlled motion of profits in a chaotic economic model, DYNA Dynamics and Applications - September 8-12, 2008, Universidade do Minho, Braga, Portugal. (With Cristina Januário, Diana A. Mendes and Clara Grácio) [11] The chaotic motion of profits in a structure of a firm: measure and control, European Conference on Iteration Theory, September 7 13, 2008, Yalta, Ukraine. (With Diana A. Mendes, Cristina Januário and Clara Grácio) [10] Jorge Duarte, Ecological complexity: evaluation and control of stoichiometric chaos, ECMTB08- European Conference on Mathematical and Theoretical Biology - 29th June - 4th July, 2008, Edinburgh, Scotland (U.K). (With Cristina Januário and Nuno Martins) [9] Jorge Duarte, Ecological complexity: Chaos in a three species food chain model, Nonlinear Dynamics and Chaos: Advances and Perspectives - September 17-21, 2007, Aberdeen, Scotland (U.K). (With Cristina Januário and Nuno Martins) [8] Jorge Duarte, Low-dimensional dynamics of a chaotic food chain model, NEEDS 2007 Nonlinear Evolution and Dynamical Systems - June 16-23, L Ametlla de Mar, 2007, Barcelona, Spain. (With Cristina Januário and Nuno Martins) [7] Jorge Duarte, The effect of coupling on identical bursting cells, ICDEA 2005 International Conference on Difference Equations and Applications - July 25-30, 2005, Munich, Germany. (With J. Sousa Ramos)

5 [6] Jorge Duarte, Computation of the topological entropy in chaotic biophysical bursting models for excitable cells, ECMTB European Conference on Mathematical and Theoretical Biology - July 18-22, 2005, Dresden, Germany. (With J. Sousa Ramos) [5] Jorge Duarte, Low-dimensional dynamics of cardiac arrhythmias, ECIT European Conference on Iteration Theory - August 29 September 04, 2004, Batschuns, Austria. (With J. Sousa Ramos) [4] Jorge Duarte, Symbolic dynamics in the study of bursting electrical activity, 9 th International Conference on Difference Equations and Applications, University of Southern California, Los Angeles, August 2-6, 2004, California (USA). (With J. Sousa Ramos) [3] Jorge Duarte, Bifurcations associated with the Fitzhugh-Nagumo equations NDES th International IEEE Workshop on Nonlinear Dynamics of Electronic Systems Centro de Geofísica, Universidade de Évora, 9-13 May 2004, Évora, Portugal. (With J. Sousa Ramos) [2] Jorge Duarte, Discrete Dynamics of the Fitzhugh-Nagumo Systems, XIV International Congress on Mathematical Physics, July 28 August 2, 2003, Lisbon, Portugal. (With J. Sousa Ramos) [1] Jorge Duarte, Topological invariants in forced piecewise-linear Fitzhugh-Nagumo-like systems, International Conference Dynamical Systems, University of North Texas, May 25 29, 2003, Denton (USA). (With J. Sousa Ramos) INTERNATIONAL COURSES AND WORKSHOPS Biomathematics Euro Summer School Dynamical Systems in Physiology and Medicine, organized by the European Society of Mathematical and Theoretical Biology, Urbino (Italy), July 8 th -19 th, 2002 VIII Jornadas Andaluzas de Educação Matemática - "Thales", Universidad de Jaen (Spain) September, 1998 INVITED RESEARCH STAYS IN INTERNATIONAL CENTRES Barcelona Biomedical Research Park, Complex Systems Lab, Barcelona (Spain), November 13 th -15 th, 2008 Barcelona Biomedical Research Park, Complex Systems Lab, Barcelona (Spain), April 9 th -14 th, 2009 Barcelona Biomedical Research Park, Complex Systems Lab, Barcelona (Spain), June 5 th -7 th, 2009 Universitat Politècnica de València (UPV) Valencia (Spain), November 13 th -15 th, 2009 Universitat Politècnica de València (UPV) Valencia (Spain), February 4 th -8 th, 2010 Universitat Politècnica de València (UPV) Valencia (Spain), May 13 th -16 th, 2010 Universitat Politècnica de València (UPV) Valencia (Spain), July 19 th -22 nd, 2010

6 Universitat Politècnica de València (UPV) Valencia (Spain), September 14 th -18 th, 2010 Universitat Politècnica de València (UPV) Valencia (Spain), November 25 th -29 th, 2010 Universitat Politècnica de València (UPV) Valencia (Spain), January 20 th -23 th, 2011 SUPERVISED PhD THESIS Carla Cristina Morbey Rodrigues (University of Évora) (Began in 2010) Thesis Co-supervised together with Carlos Correia Ramos (University of Évora) and Josep Sardanyés (Universitat Politècnica de València) MEMBER OF PhD THESIS JURIES João M. Cabral, Analitical and symbolic study of bifurcations for the family of maps of degree two, Department of Mathematics, University of Azores, October 16 th, 2009 REFEREE FOR INTERNATIONAL SCIENTIFIC JOURNALS Referee for the following Journals: - Chaos: an Interdisciplinary Journal of Nonlinear Science - Simulations Modeling Practice and Theory PROFESSIONAL MEMBERSHIPS Member of the Portuguese Society of Mathematics (SPM) Member of the European Society for Mathematical and Theoretical Biology (ESMTB) Last modification in January 2011