2020 applicants
People

Dr Chris Antonopoulos

Lecturer
Department of Mathematical Sciences
Dr Chris Antonopoulos
  • Email

  • Telephone

    +44 (0) 1206 873018

  • Location

    STEM 5.8, Colchester Campus

  • Academic support hours

    You may contact me by email

Profile

Biography

I joined the Department of Mathematical Sciences at the University of Essex in 2015, and I am currently a lecturer in Applied Mathematics. My research is focused on using novel mathematical and computational techniques to study problems in dynamical systems, chaotic systems, computational neuroscience, complex systems and complex networks. In particular, one of my main interests is in computational neuroscience, and specifically in the development of approaches and mathematical tools that give insights into the inner workings of the brain. My current main focus is on studying the emergence of synchronisation phenomena in the brain using concepts from dynamical systems, nonlinear dynamics, chaos theory, information theory, complex systems and complex networks. The idea is to develop mathematical tools to analyse neural activity and collective behaviour in the brain in order to gain insights into its inner workings. This is primarily related to establishing the relationship between neural synchronisation and brain plasticity, as excessive bursting synchronisation in the plastic brain underpins brain disorders such as Parkinson’s and epilepsy. Another main focus of my work is on network inference using mathematical and information-theoretical approaches. The idea being the inference of the connectivity of the nodes in a network, when only access to recorded data on the nodes of the network (e.g. in the form of time-series) is available. The data may be experimental, may come from EEG studies, from coupled dynamical systems, or from other sources. Possible applications include brain functional connectivity, social networks, biological networks, etc. Related to these projects is my work on how synchronisation phenomena and chimera-like states, a peculiar synchronisation phenomenon observed in artificial systems, experiments and for example, in the brain of dolphins, macaque monkeys and birds, emerge in dynamical systems given by nonlinear systems of coupled ordinary differential equations. The main focus here is to develop mathematical approaches to understand better how synchronisation phenomena give rise to the emergence of collective behaviour in complex systems, such as the brain. This approach involves the study of the behaviour of individual components (microscopic analysis), all the way up to the study of the macroscopic behaviour attributed to the individual components of the system and to their connectivity. In parallel, I am working on the mathematical properties and long-term behaviour of dynamical systems given by nonlinear systems of coupled ordinary differential equations. These can be either dissipative or conservative, lower- or higher-dimensional. As these systems can rarely be solved analytically to obtain their solutions in closed form, this research involves the use of a combination of analytical and numerical approaches. I am interested in studying the structure of their state spaces and long-term dynamics. In doing so, I am using Lyapunov exponents, chaotic indicators (SALI, GALI, LDI, etc.), stability analysis of fixed points and periodic orbits, and bifurcation analysis, among other approaches. I am also working on ordered, weakly chaotic and chaotic dynamics in multi-dimensional Hamiltonian systems and on their connection to entropy and q-statistics, associated to non-extensive Statistical Mechanics. The focus here is on studying how energy spreads in Hamiltonian lattices, representing chains of particles, in various regimes and whether it equilibrates in the thermodynamic limit, a long-debated question in the field. The work in the project is supported by techniques such as Lyapunov spectra, chaotic indicators (SALI, GALI, LDI, etc.), stability analysis of fixed points and periodic orbits, and bifurcation analysis. This research also involves the use of a combination of analytical and numerical approaches, involving but not limited to symplectic integrators. Recently, I have developed an interest in studying mathematically the spread of COVID-19 in communities, for example, in countries, states, etc., modelling published data using for example, the SIR and extended versions of the SIR models. The project focuses on forecasting reliably the spread of the disease, including the possibility of surges in the susceptible population. This involves studying different approaches and scenarios to confine the spread and eventually halt it, contributing thus to the well-being of communities and individuals. The truly interdisciplinary nature of my research means that I work with a range of collaborators from different fields and backgrounds. I believe in the value of communicating scientific research, and in the role that mathematics and quantitative approaches can play in my research. To this end, I have organised a range of mini-symposia, have presented my work as invited speaker in international conferences, have become editor in peer-reviewed journals and have delivered high-profile public engagement talks. I am an elected Member of the Institute of Mathematics and its Applications (MIMA), and member of the London (LMS), Edinburgh (EMS) and European (EuMS) Mathematical Societies. I am also a Fellow of the Higher Education Academy (FHEA).

Qualifications

  • BSc in Mathematics University of Crete, (1999)

  • MSc in Dynamical Systems and Differential Equations University of Patras, (2002)

  • PhD (thesis: "Stability and chaos in Hamiltonian systems of many degrees of freedom: From classical to statistical mechanics") University of Patras, (2007)

Appointments

University of Essex

  • Lecturer in Applied Mathematics, Department of Mathematical Sciences, University of Essex (15/9/2015 - present)

Other academic

  • Research Fellow (EPSRC), Department of Physics (ICSMB), University of Aberdeen (12/10/2012 - 31/8/2015)

  • Post Doctoral Researcher, Department of Mathematics, University of Patras (1/9/2010 - 31/12/2012)

  • Post Doctoral Researcher, Service de Physique des Systèmes Complexes et Mécanique Statistique, Université Libre de Bruxelles (1/10/2008 - 30/9/2010)

Research and professional activities

Research interests

Mathematical modelling of the brain

In this project, I am interested in modelling and studying the brain mathematically, combining concepts from dynamical systems, chaos theory, nonlinear dynamics, complex networks, complex systems and synchronisation theory. I am fascinated by its inner workings and am developing mathematical approaches to study and better understand. Prospective PhD students who want to work on the project, are welcome to contact me for further details.

Key words: Ordinary differential equations
Open to supervise

Mathematical approaches to infer network connectivity

In this project, I am working on network inference using mathematical and information-theoretical approaches. We want to infer the connectivity of the nodes in a network, when we only have access to recorded data on the nodes of the network (e.g. in the form of time-series). The data may be experimental, may come from EEG studies, from coupled dynamical systems, or from other sources. Possible applications include brain functional connectivity, social networks, biological networks, etc. Prospective PhD students who want to work on the project, are welcome to contact me for further details.

Key words: Networks
Open to supervise

Multi-dimensional Hamiltonian systems, chaotic dynamics and complex statistics

In this project, I am studying, ordered, weakly chaotic and chaotic dynamics in multi-dimensional Hamiltonian systems and their connection to entropy and q-statistics, associated to non-extensive Statistical Mechanics. We want to understand how energy spreads in Hamiltonian lattices, representing chains of particles, in various regimes and whether it equilibrates in the thermodynamic limit, a long-debated question in the field. Techniques used are Lyapunov spectra, chaotic indicators (SALI, GALI, LDI, etc.), stability analysis of fixed points and periodic orbits, and bifurcation analysis, among other approaches. This research also involves the use of a combination of analytical and numerical approaches, involving but not limited to symplectic integrators. Prospective PhD students who want to work on the project, are welcome to contact me for further details.

Key words: Hamiltonian systems
Open to supervise

Mathematical modelling of the spread of COVID-19 in communities

In this project, I am conducting fascinating research on the spread of COVID-19 in communities (for example, in countries, states, etc.), modelling published data using for example, the SIR and extended versions of the SIR models. We want to forecast reliably the spread of the disease, including the possibility of surges in the susceptible population. We aim to studying different approaches and scenarios to confine the spread and eventually halt it, contributing thus to the well-being of communities and individuals. Prospective PhD students who want to work on the project, are welcome to contact me for further details.

Key words: COVID-19
Open to supervise

Nonlinear dynamics and long-term behaviour

In this project, I am studying the mathematical properties and long-term behaviour of dynamical systems given by nonlinear systems of coupled ordinary differential equations. These can be either dissipative or conservative, lower- or higher-dimensional. As these systems can rarely be solved analytically to obtain their solutions in closed form, this research involves the use of a combination of analytical and numerical approaches, involving but not limited to numerical integrators. I am interested in studying the structure of their state spaces and long-term dynamics. Techniques used are Lyapunov spectra, chaotic indicators (SALI, GALI, LDI, etc.), stability analysis of fixed points and periodic orbits, and bifurcation analysis, among other approaches. Prospective PhD students who want to work on the project, are welcome to contact me for further details.

Key words: Dynamical systems
Open to supervise

Synchronisation, chimera-like states and emergence of collective behaviour in complex systems

In this project, I am conducting fascinating research on how synchronisation phenomena and chimera-like states, a peculiar synchronisation phenomenon observed in artificial systems, experiments and for example, in the brain of dolphins, macaque monkeys and birds, emerge in dynamical systems given by nonlinear systems of coupled ordinary differential equations. My goal is to develop mathematical approaches to understand better how synchronisation phenomena give rise to the emergence of collective behaviour in complex systems, such as the brain. This approach involves the study of the behaviour of individual components (microscopic analysis), all the way up to the study of the macroscopic behaviour attributed to the individual components of the system and to their connectivity. Prospective PhD students who want to work on the project, are welcome to contact me for further details.

Key words: Synchronisation
Open to supervise

Teaching and supervision

Current teaching responsibilities

  • Classical Mechanics (MA222)

  • Advanced Ordinary Differential Equations (MA307)

Previous supervision

Awatf Kidher Mohammed Ali Alwiya
Awatf Kidher Mohammed Ali Alwiya
Thesis title: Mathematical Modelling and Brain Dynamical Networks
Degree subject: Applied Mathematics
Degree type: Doctor of Philosophy
Awarded date: 6/7/2020
Mikaela Joanne Webster
Mikaela Joanne Webster
Degree subject: Mathematics
Degree type: Master of Science
Awarded date: 5/10/2016

Publications

Journal articles (41)

Protachevicz, PR., Santos, MS., Seifert, EG., Gabrick, EC., Borges, FS., Borges, RR., Trobia, J., Szezech Jr, JD., Iarosz, KC., Caldas, IL., Antonopoulos, CG., Xu, Y., Viana, RL. and Batista, AM., Noise induces continuous and noncontinuous transitions in neuronal interspike intervals range. Pramana: journal of physics

Borges, FS., Protachevicz, PR., Pena, RFO., Lameu, EL., Higa, GSV., Kihara, AH., Matias, FS., Antonopoulos, CG., de Pasqual, R., Roque, AC., Iarosz, KC., Ji, P. and Batista, AM., (2020). Self-sustained activity of low firing rate in balanced networks. Physica A: Statistical Mechanics and its Applications. 537, 122671-122671

Cooper, I., Mondal, A. and Antonopoulos, CG., (2020). A SIR model assumption for the spread of COVID-19 in different communities. Chaos, Solitons and Fractals. 139, 110057-110057

Ghosh, S., Mondal, A., Ji, P., Mishra, A., Kumar Dana, S., Antonopoulos, C. and Hens, C., (2020). Emergence of mixed mode oscillations in random networks of diverse excitable neurons: the role of neighbors and electrical coupling. Frontiers in Computational Neuroscience. 14, 1-11

Cooper, I., Mondal, A. and Antonopoulos, CG., (2020). Dynamic tracking with model-based forecasting for the spread of the COVID-19 pandemic. Chaos, Solitons and Fractals. 139, 110298-110298

Basios, V. and Antonopoulos, CG., (2019). Hyperchaos & labyrinth chaos: revisiting Thomas-Rössler systems. Journal of Theoretical Biology. 460, 153-159

Protachevicz, PR., da Silva Borges, F., Lameu, EL., Ji, P., Iarosz, KC., Kihara, AH., Caldas, IL., Szezech, JD., Baptista, MS., Macau, EEN., Antonopoulos, C., Batista, AM. and Kurths, J., (2019). Bistable firing pattern in a neural network model. Frontiers in Computational Neuroscience. 13 (19), 19-

Antonopoulos, CG., Martinez-Bianco, E. and Baptista, M., (2019). Evaluating performance of neural codes in model neural communication networks. Neural Networks. 109, 90-102

Goh, YK., Hasim, HM. and Antonopoulos, CG., (2018). Inference of financial networks using the normalised mutual information rate.. PloS one. 13 (2), e0192160-e0192160

Antonopoulos, CG. and Shang, Y., (2018). Opinion formation in multiplex networks with general initial distributions.. Scientific reports. 8 (1), 2852-

Borges, RR., Borges, FS., Lameu, EL., Batista, AM., Iarosz, KC., Caldas, IL., Antonopoulos, CG. and Baptista, MS., (2017). Spike timing-dependent plasticity induces non-trivial topology in the brain.. Neural networks : the official journal of the International Neural Network Society. 88, 58-64

Antonopoulos, CG. and Baptista, MS., (2017). Maintaining extensivity in evolutionary multiplex networks.. PloS one. 12 (4), e0175389-e0175389

Antonopoulos, CG., Skokos, C., Bountis, T. and Flach, S., (2017). Analyzing chaos in higher order disordered quartic-sextic Klein-Gordon lattices using q-statistics. Chaos, Solitons and Fractals. 104, 129-134

Antonopoulos, CG., Fokas, AS. and Bountis, TC., (2016). Dynamical complexity in the C.elegans neural network. European Physical Journal: Special Topics. 225 (6-7), 1255-1269

Bianco-Martinez, E., Rubido, N., Antonopoulos, CG. and Baptista, MS., (2016). Successful network inference from time-series data using Mutual Information Rate. Chaos: an interdisciplinary journal of nonlinear science. 26 (4), 043102-043102

Antonopoulos, CG., (2016). Dynamic range in the C. elegans brain network.. Chaos (Woodbury, N.Y.). 26 (1), 013102-013102

Hizanidis, J., Kouvaris, NE., Zamora-López, G., Díaz-Guilera, A. and Antonopoulos, CG., (2016). Chimera-like states in modular neural networks. Scientific Reports. 6 (19845), 19845-

Antonopoulos, CG., Bountis, T. and Drossos, L., (2016). Coupled symplectic maps as models for subdiffusive processes in disordered Hamiltonian lattices. Applied Numerical Mathematics. 104, 110-119

Antonopoulos, CG., Srivastava, S., Pinto, SEDS. and Baptista, MS., (2015). Do brain networks evolve by maximizing their information flow capacity?. PLOS Computational Biology. 11 (8), e1004372-e1004372

Hizanidis, J., Kouvaris, NE. and Antonopoulos, CG., (2015). Metastable and chimera-like states in the C.elegans brain network. Cybernetics and Physics. 4 (1), 17-20

Antonopoulos, CG., Bianco-Martinez, E. and Baptista, MS., (2014). Production and transfer of energy and information in Hamiltonian systems.. PloS one. 9 (2), e89585-e89585

Antonopoulos, CG., Michas, G., Vallianatos, F. and Bountis, T., (2014). Evidence of q-exponential statistics in Greek seismicity. Physica A: Statistical Mechanics and its Applications. 409, 71-77

Antonopoulos, CG., Bountis, T., Skokos, C. and Drossos, L., (2014). Complex statistics and diffusion in nonlinear disordered particle chains.. Chaos (Woodbury, N.Y.). 24 (2), 024405-024405

Antonopoulos, C., Basios, V., Demongeot, J., Nardone, P. and Thomas, R., (2013). Linear and nonlinear arabesques: A study of closed chains of negative 2-element circuits. International Journal of Bifurcation and Chaos. 23 (9), 1330033-1330033

Manos, T., Skokos, C. and Antonopoulos, C., (2012). Probing the local dynamics of periodic orbits by the Generalized Alignment Index (GALI) method. International Journal of Bifurcation and Chaos. 22 (09), 1250218-1250218

Bountis, T., Manos, T. and Antonopoulos, C., (2012). Complex statistics in Hamiltonian barred galaxy models. Celestial Mechanics and Dynamical Astronomy. 113 (1), 63-80

García Cantú Ros, A., Antonopoulos, CG. and Basios, V., (2011). Emergence of coherent motion in aggregates of motile coupled maps. Chaos, Solitons and Fractals. 44 (8), 574-586

Antonopoulos, C. and Christodoulidi, H., (2011). Weak chaos detection in the Fermi–Pasta–Ulam-α system using q-Gaussian statistics. International Journal of Bifurcation and Chaos. 21 (08), 2285-2296

Antonopoulos, C., Bountis, T. and Basios, V., (2011). Quasi-stationary chaotic states in multi-dimensional Hamiltonian systems. Physica A: Statistical Mechanics and its Applications. 390 (20), 3290-3307

Antonopoulos, C., Basios, V. and Bountis, T., (2010). Weak chaos and the "melting transition" in a confined microplasma system.. Physical review. E, Statistical, nonlinear, and soft matter physics. 81 (1 Pt 2), 016211-

Petalas, YG., Antonopoulos, CG., Bountis, TC. and Vrahatis, MN., (2009). Detecting resonances in conservative maps using evolutionary algorithms. Physics Letters, Section A: General, Atomic and Solid State Physics. 373 (3), 334-341

Skokos, C., Bountis, T. and Antonopoulos, C., (2008). Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi--Pasta--Ulam lattices by the Generalized Alignment Index method. The European Physical Journal Special Topics. 165 (1), 5-14

Petalas, YG., Antonopoulos, CG., Bountis, TC. and Vrahatis, MN., (2008). Evolutionary methods for the approximation of the stability domain and frequency optimization of conservative maps. International Journal of Bifurcation and Chaos. 18 (8), 2249-2264

Skokos, C., Bountis, TC. and Antonopoulos, C., (2007). Geometrical properties of local dynamics in Hamiltonian systems: The Generalized Alignment Index (GALI) method. Physica D: Nonlinear Phenomena. 231 (1), 30-54

Antonopoulos, C., Bountis, T. and Skokos, C., (2006). Chaotic dynamics of N-degree of freedom Hamiltonian systems. International Journal of Bifurcation and Chaos. 16 (06), 1777-1793

Antonopoulos, C. and Bountis, T., (2006). Stability of simple periodic orbits and chaos in a Fermi-Pasta-Ulam lattice.. Physical review. E, Statistical, nonlinear, and soft matter physics. 73 (5 Pt 2), 056206-

Antonopoulos, C. and Bountis, T., (2006). Detecting order and chaos by the Linear Dependence Index (LDI) method. ROMAI Journal. 2 (2), 1-13

Petalas, YG., Antonopoulos, C., Bountis, T. and Vrahatis, MN., (2006). Detecting resonances using evolutionary algorithms. Recent Progress in Computational Sciences and Engineering. 7A-B, 443-443

Skokos, C., Antonopoulos, C., Bountis, TC. and Vrahatis, MN., (2004). Detecting order and chaos in Hamiltonian systems by the SALI method. Journal of Physics A: Mathematical and General. 37 (24), 6269-6284

Skokos, C., Antonopoulos, C., Bountis, TC. and Vrahatis, M., (2003). How does the Smaller Alignment Index (SALI) distinguish order from chaos?. Progress of Theoretical Physics Supplement. 150 (150), 439-443

Rothos, VM., Antonopoulos, C. and Drossos, L., (2002). Chaos in a near-integrable Hamiltonian lattice. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 12 (8), 1743-1754

Book chapters (2)

Christodoulidi, H., Van Der Weele, K., Antonopoulos, CG. and Bountis, T., (2014). Phase transitions in models of bird flocking. In: Chaos, Information Processing and Paradoxical Games: The Legacy of John S. Nicolis. WORLD SCIENTIFIC. 383- 398. 9789814602129

Antonopoulos, C., Skokos, C., Bountis, T. and Vrahatis, MN., (2003). A fast and reliable method for distinguishing regular from chaotic motion in Hamiltonian systems. In: Recent Advances in Mechanics and Related Fields. University of Patras. 325- 333

Conferences (6)

Sigalas, E., Li, J., Bezerianos, A. and Antonopoulos, C., (2018). Emergence of chimera-like states in prefrontal-cortex macaque intracranial recordings

Petalas, YG., Antonopoulos, C., Bountis, T. and Vrahatis, MN., (2007). Ανίχνευση συντονισμών σε διατηρητικές απεικονίσεις με τη χρήση εξελικτικών αλγορίθμων (Detecting resonances in conservative maps using evolutionary algorithms)

Antonopoulos, C., Petelas, YG., Bountis, T. and Vrahatis, MN., (2005). Υπολογισμός της δυναμικής ακτίνας ευστάθειας συμπλεκτικών απεικονίσεων με χρήση εξελικτικών αλγορίθμων (Calculation of the dynamic aperture of stability of symplectic maps using evolutionary algorithms)

Antonopoulos, C., Manos, T. and Skokos, C., (2004). SALI: An efficient indicator of chaos with application to 2 and 3 degrees of freedom Hamiltonian systems

Skokos, C., Antonopoulos, C., Bountis, TC. and Vrahatis, MN., (2003). Smaller Alignment Index (SALI): Determining the ordered or chaotic nature of orbits in conservative dynamical systems

Skokos, C., Antonopoulos, C., Bountis, TC. and Vrahatis, MN., (2002). Smaller Alignment Index (SALI): Detecting Order and Chaos in Conservative Dynamical Systems

Grants and funding

2020

Modelling brain activity: reconciling empirical imaging data with network inference and dynamics with an outlook on Alzheimers's disease

Institut Henri Poincar�

2019

Studying the emergence of chimera states and self-organisation in dynamical networks

London Mathematical Society

Contact

canton@essex.ac.uk
+44 (0) 1206 873018

Location:

STEM 5.8, Colchester Campus

Academic support hours:

You may contact me by email