**Prof. Rajarshi Roy**, **University of Maryland**

### Complex Photonics Dynamics: counting single photons, birthing chaotic attractors, and generating random numbers

### November 28, 2022 – 8:30 PM IST

**Abstract**: Light conveys energy and information and is a primary means of communication today. Dr. Rajarshi Roy will describe concepts and experiments that have revealed new aspects of light and its interaction with matter, including synchronization of light sources and the communication of information. Detecting single photons can reveal how a system with complex photonic dynamics can transition from a Poisson process to a chaotic attractor. The application of time-delayed feedback to produce chaotic dynamics at extreme speeds and generate random numbers will illustrate an unexpected benefit of chaotic dynamics. Quantum fluctuations are random seeds amplified to macroscopic levels in a deterministic system.

**Rajarshi Roy** studied Physics at St. Stephen’s College in Delhi, India, and received a Ph.D. in Physics from the University of Rochester in 1981. He has advised about forty doctoral students at Georgia Tech (1982 – 1999) and the University of Maryland (1999 – present). He has served as chair of the School of Physics at Georgia Tech (1996 – 1999) and Director of the Institute for Physical Science and Technology (2003 – 2014) at the University of Maryland. He is a professor in the Department of Physics and the Institute for Physical Science and Technology. He was a visitor at Bell Labs in Murray Hill in the spring of 1987, a visitor at NIH in 2009 and 2014, and Benedict Distinguished Visiting Professor at Carleton College in 2020 for the fall semester. He is a fellow of the Optical Society of America (now Optica) and the American Physical Society.

**Prof. Ginestra Bianconi**, **Queen Mary University of London**

### The dynamics of higher-order networks: the effect of topology and triadic interactions

### November 7, 2022

**Abstract**: Higher-order networks capture the interactions among two or more nodes in complex systems ranging from the brain to chemical reaction networks. In this talk, Prof. Bianconi will show that higher-order interactions are responsible for new dynamical processes that cannot be observed in pairwise networks. She will cover how topology is key to defining the synchronization of topological signals, i.e. dynamical signals defined not only on nodes but also on links, triangles, and higher-dimensional simplices in simplicial complexes. Interesting topological synchronization dictated by the Dirac operator can lead to the spontaneous emergence of a rhythmic phase where the synchronization order parameter displays low frequency oscillations which might shed light on possible topological mechanisms for the emergence of brain rhythms. She will also reveal how triadic interactions can turn percolation into a fully-fledged dynamical process in which nodes can turn on and off intermittently in a periodic fashion or even chaotically leading to period doubling and a route to chaos of the percolation order parameter.

**Ginestra Bianconi** is a Professor of Applied Mathematics in the School of Mathematical Sciences of the Queen Mary University of London, and she is Alan Turing Fellow at the Alan Turing Institute. Currently, she is Chief Editor of JPhys Complexity, Editor of PloSOne, and Scientific Reports, and she is Associate Editor of Chaos, Solitons, and Fractals. Award: Network Science Fellowships by the NetSci Society. Her research activity on Statistical Mechanics and Network Science includes Network Theory and its interdisciplinary applications. She has formulated the Bianconi-Barabasi model that displays the Bose-Einstein condensation in complex networks. She has formulated the statistical mechanics of network ensembles and she has proven their non-equivalence. She has made important contributions on the study of critical phenomena on networks. In the last years, she has been focusing on multilayer networks, simplicial complexes, network geometry and topology, percolation, synchronization, and network control. She is the author of the books Multilayer Networks: Structure and Function (Oxford University Press, 2018), Higher-order Networks: An introduction to simplicial complexes (Cambridge University Press, 2021), and editor of Networks of Networks in Biology (Cambridge University Press, 2021).

Photo credits: https://twitter.com/netsci2020/status/1306125360761888768?s=20&t=4e5hotNaZK0WZ2FESrrANQ

**Prof. Tomasz Kapitaniak**, **Lodz University of Technology**

### Chimera states for coupled pendula

### September 26, 2022

**Abstract**: Chimera states are one of the most intriguing phenomena in complex dynamical systems. Typically, they are identified by the co-existence of two types of patterns within one network scheme: (i) a regular behavior, which corresponds to partial synchronization of system’s units, and (ii) an irregular one, when the motion of a group of oscillators is related to the chaotic dynamics. Both domains can co-exist, even though the topology of coupling is usually symmetrical. This surprising fact shows, that by combining both coherence and incoherence, chimeras become one of the most fundamental structures in the area of modern, nonlinear problems. Chimera states can be found in a variety of dynamical systems, beginning from such fundamental ones as the Kuramoto model, for which they have been originally described, or coupled pendula. The studies on chimeras in chemical oscillators, neuron networks, or delayed systems, as well as the experimental proofs of their existence have shown, that this type of behavior is interdisciplinary and appears universally in different areas of science.

In this study, we consider the dynamics of different networks of pendula: (i) a star network of N+1 nonlinear oscillators (in such networks, there is one central hub node (labeled by site index i=N+1) and N environmentally identical peripheral end–nodes connected to the central one (labeled by indices i=1,…, N)), (ii) a network of locally coupled pendula (each pendulum is connected with the nearest neighbor by the spring and damper elements), (iii) a network of globally coupled pendula (each pendulum is connected with all other pendula by the spring and damper elements). For each network, the route from complete incoherence to coherence is described. A particular attention is paid to the occurrence of the chimera states. Numerical results are partially confirmed experimentally.

**Tomasz Kapitaniak** is a professor of theoretical and applied mechanics and head of the Division of Dynamics at Lodz University of Technology since 1992. His research is concentrated on nonlinear dynamics. The development of non-feedback methods for chaos control, identification and description of new types of bifurcations, identification of the synchronization mechanism in coupled mechanical oscillators, and the explanation of the origin of randomness in mechanical systems are among his most important scientific discoveries. In 2013 he was elected a member of the Polish Academy of Sciences. He got Doctor Honoris Causa degrees at the Saratov State University (Russia) and Lublin University of Technology (Poland) respectively in 2001 and 2014.

Photo credits: https://p.lodz.pl/en/research/most-prominent-scientists/professor-tomasz-kapitaniak

**Dr. Viola Priesemann**, MPIDS Göttingen

### Spreading dynamics: from neural information flow to COVID-19

#### May 30, 2022

**Abstract**: Spreading dynamics is ubiquitous: activity spreads in neural networks, news and fake news in social networks, and just recently the spread of a novel virus has disrupted the daily lives of people around the globe. Interestingly, in all these networks, the connections are not static but change over time, e.g., to implement learning in neural networks or when mitigating the spread of SARS-CoV-2. Dr. Priesemann and her group derive the principles of self-organization in these diverse networks, show under which conditions phase transitions and critical phenomena occur, and how these can optimize information flow. Her team then puts these theoretical results to the test in living real-world networks. Overall, their work contributes to our understanding of the self-organization of living systems, from information flow in neural networks to the infodemics-pandemics interaction in social networks.

**Viola Priesemann** is a physicist and neuroscientist at the Max Planck Institute for Dynamics and Self-Organization, Göttingen. After research projects at the Ecole Normale Superieure Paris (France) and the Caltech (USA), she obtained her Ph.D. at the MPI for Brain Research and the University of Frankfurt. As a postdoc and Fellow at the Bernstein Center Göttingen, she applied for an independent Max Planck Research Group, which started in 2017 at the MPI in Göttingen. She studies self-organization and learning in living and artificial networks, illuminating the basic mechanisms that shape collective information processing. Since the start of the COVID-19 pandemic, she investigated the spread of SARS-CoV-2, quantified the effectiveness of interventions, and derived containment strategies. She has coordinated several position and overview papers on the COVID-19 pandemic and is a member of the advisory board of the German government. Her work has been recognized by several awards, including the Communitas Award of the Max-Planck-Society, the “Niedersächsische Wissenschaftspreis”, the “Medaille für naturwissenschaftliche Publizistik” of the German Physical Society (DPG), and the Dannie-Heineman-Award. She is a board member of the Campus Institute for Data Science, a member of the Cluster of Excellence “Multiscale Bioimaging”, of the Max Planck – University of Toronto Centre for Neural Science and Technology, and of “Die Junge Akademie” of the National Academy.

Photo credits: https://uni-goettingen.de/de/priesemann%2C+viola%2C+dr.+-+theorie+neuronaler+systeme+(mpi-ds)/622913.html

**Prof. M. Lakshmanan**, Bharathidasan U.

### Integrability and Chaos in Simple and Complex Systems

#### April 25, 2022

**Abstract:** In my talk, I will present a broad overview of some of the fascinating collective dynamical states which arise in the study of integrable and nonintegrable, including chaotic, nonlinear systems of simple and complex types, and illustrate them with specific examples. These include degenerate and nondegenerate solitons, breathers, rogue waves, bullets, and vortices in nonlinear dispersive systems, and desynchronized states, synchronized states, clusters, chimeras, traveling and solitary waves, chimera death states, and so on in complex nonlinear dissipative dynamical systems. Suitable characterizing measures such as strength of inhomogeneity, discontinuity measure, strength of mixed synchronization symmetry, etc. will be introduced to describe the latter states. Some applications in nonlinear optical systems, magnetic spin systems/spintronics, nonlinear electronic circuits, and mechanical systems including Mathews- Lakshmanan oscillator, Liénard type nonlinear oscillator, and Murali-Lakshmanan-Chua circuit will be touched upon.

**Prof. Muthusamy Lakshmanan** specializes in the areas of Nonlinear Dynamics/Theoretical Physics with special reference to solitons, nonlinear evolution equations, and chaos. He has made varied and in-depth contributions to the general theory of solitons, integrable systems, magnetic and optical solitons, and classical chaos including bifurcations, control, synchronization, and secure communications, as well as quantum chaos and spatiotemporal patterns. Known for his research on nonlinear dynamics and for the development of *Murali-Lakshmanan-Chua (MLC) Circuit*, Professor Lakshmanan is a Fellow of all the three Academies of Science of India and is an elected Foreign Member of the Royal Academy of Sciences, Uppsala, Sweden. He is also an elected Fellow of the Academy of Sciences of the Developing Countries (FTWAS 2009).

Photo credits: https://en.wikipedia.org/wiki/Muthusamy_Lakshmanan

**Prof. Katharina Krischer**, TU Munich

Between Synchrony and Turbulence: The Rich Dynamics of Globally Coupled Stuart-Landau Oscillators

#### March 28, 2022

**Abstract**: Ensembles of coupled oscillators are a class of seemingly simple dynamical systems that can take on a rich variety of emergent behaviors and have provided insights in virtually every discipline, from the natural sciences to sociology. In many studies, weak coupling between the oscillators has been assumed. In this case, the dynamics of an individual oscillator can be approximated by the evolution of its phase only, and emergent behavior is studied in the framework of coupled phase oscillators, such as the famous Kuramoto model. In this talk, Prof. Krischer will consider situations where the phase approximation breaks down, and the dynamics of the ensemble is instead captured by coupled Stuart-Landau oscillators. First, Prof. Krischer will focus on 2-cluster states and discuss that all possible 2-cluster states emerge from a codimension-2 bifurcation, the so-called cluster singularity, which acts as organizing center for the saddle-node bifurcations creating the 2-cluster states as well as for transverse bifurcations alternating their stability. When coupled nonlinearly, two-cluster states can further differentiate in cluster-splitting cascades, leading to multi-cluster states of widely different sizes. These states may then collide with mirror images in phase space, destroying some of the clusters and rendering the dynamics chaotic. A cascade of such symmetry-increasing bifurcations eventually produces a completely incoherent state in which each oscillator has its own asynchronous dynamics. The penultimate state of this cascade consists of one large synchronized cluster and otherwise only individual oscillators, i.e., a so-called chimera state. Chimera states have received much attention during the last decade. In our example, it is thus just one state of two cascades of other coexistence states that link the synchronous state to a state of complete incoherence.

**Prof. Katharina Krischer** investigates fundamental aspects of self-organization and pattern formation under non-equilibrium conditions. Her work includes experiments, which mainly focus on nonlinear phenomena at the solid/liquid interface, and theory. In the theoretical work she bridges the gap between system specific models and normal form type approaches. Since 2002 she is a professor of physics at the Technical University of Munich, Germany, and has

coauthored about 130 publications in peer reviewed journals as well as a text book on ‘Physics of Energy Conversion’. She was elected a fellow of the International Society of Electrochemistry and is a member of the German Physical Society (DPG) and the Society of German Chemists (GDCh).

Photo credits: https://www.ph.tum.de/about/diversity/gender/?language=en

**Dr. Louis Pecora**, NRL Washington (with Dr. Thomas L. Carroll)

Statistics of Attractor Embeddings in Reservoir Computing

#### February 28, 2022

**Abstract: **The question why a reservoir computer (RC), driven by only one time series from a drive system, can be trained to recreate all dynamical time series signals from the drive leads to the idea that the RC must be recreating the attractor from the drive signal, i.e. creating an embedding of the drive attractor in the RC dynamics. There have been some mathematical advances that move that argument closer to a general theorem. However, for RCs constructed from actual physical systems like interacting lasers or analog circuits, the RC dynamics may not be known well or known at all. And many of the existing embedding theorems have restrictive assumptions on the dynamics. We first show that the best way to analyze RC behavior is to first treat it properly like a dynamical system, which it is. This will lead to some conflict with existing ideas about RCs, but also a clarification of those ideas. Secondly, in the absence of complete theories on RCs and attractor embeddings, we show several ways to analyze the RC behavior to help understand what underlying processes are in place, especially regarding good embeddings of the drive system in the RC. We show that a statistic we developed for other uses can help test for homeomorphisms between a drive system and the RC by using the time series from both systems. This statistic is called the continuity statistic and it is modeled on the mathematical definition of a continuous

function. We show the interplay of dynamical quantities (e.g. Lyapunov exponents, Kaplan- Yorke dimensions, generalized synchronization, etc.) and embeddings as exposed by the continuity statistic and other statistics based on ideas from nonlinear dynamical systems theory.

**Dr. Lou Pecora** is currently a research physicist at the Naval Research Laboratory, Washington, DC, where he heads the section for Magnetic Materials and Nonlinear Dynamics in the Materials and Sensors branch. He received his B.S. degree in physics from Wilkes College and he then received a PhD from Syracuse University in Solid State Science in 1977. In the same year, he was awarded an NRC postdoctoral fellowship at the Naval Research Laboratory where he worked on applications of positron annihilation techniques in determining electronic states in copper alloys. This led to a permanent position at NRL. In the mid-1980’s Dr. Pecora moved into the field of nonlinear dynamics in solid-state systems. Subsequent work has focused on the applications of chaotic behavior, especially the effects of driving systems with chaotic signals and coupling nonlinear dynamical systems in complex networks. This has resulted in the discovery of synchronization of chaotic systems, control and tracking, and dynamics of many coupled, nonlinear systems. His research interests turned to quantum chaos briefly and then to the collective behavior of oscillators in large complex networks which led to the development of the master stability function and, more recently, the use of techniques of computational group theory to study cluster synchronization. Recently, he has expanded his collective behavior research to driven networks of oscillators called reservoir computers. Dr. Pecora has published over 160 scientific papers and has 5 US patents for the applications of chaos. His original paper on the synchronization of chaotic systems has over 14000 (ISI) citations and is the 11th most cited paper ever in Physical Review Letters. In 1995 he received the Sigma Xi award for Pure Science for the study of synchronization in chaotic systems. He is also a Fellow of the American Physical Society (APS) and of the American Association for the Advancement of Science (AAAS). Recently, he and his colleague, Tom Carroll won a Clarivate Citation Award as Clarivate Laureates “Researchers of Nobel Class” by Clarivate (citation index provider) in 2020.

Photo credits: U.S. Naval Research Laboratory

**Prof. Steven Brunton**, U. Washington

### Machine Learning for Scientific Discovery, with Examples in Fluid Mechanics

#### January 31, 2022

**Abstract:** This work describes how machine learning may be used to develop accurate and efficient nonlinear dynamical systems models for complex natural and engineered systems. Prof. Brunton will explore the sparse identification of nonlinear dynamics (SINDy) algorithm, which identifies a minimal dynamical system model that balances model complexity with accuracy, avoiding overfitting. This approach tends to promote models that are interpretable and generalizable, capturing the essential “physics” of the system. He will also discuss the importance of learning effective coordinate systems in which the dynamics may be expected to be sparse. This sparse modeling approach will be demonstrated on a range of challenging modeling problems in fluid dynamics, and Prof. Brunton will discuss how to incorporate these models into existing model-based control efforts. Because fluid dynamics is central to transportation, health, and defense systems, he will emphasize the importance of machine learning solutions that are interpretable, explainable, generalizable, and that respect known physics.

**Dr. Steven L. Brunton** is a Professor of Mechanical Engineering at the University of Washington. He is also an Adjunct Professor of Applied Mathematics and Computer Science, and a Data Science Fellow at the eScience Institute. Steve received B.S. in Mathematics from Caltech in 2006 and Ph.D. in Mechanical and Aerospace Engineering from Princeton in 2012. His research combines machine learning with dynamical systems to model and control systems in fluid dynamics, biolocomotion, optics, energy systems, and manufacturing. He is a co-author of three textbooks, received the University of Washington College of Engineering junior faculty and teaching awards, the Army and Air Force Young Investigator Program (YIP) awards, and the Presidential Early Career Award for Scientists and Engineers (PECASE).

Photo credits: https://www.me.washington.edu/facultyfinder/steve-brunton

**Prof. Edward Ott**, U. Maryland

### Prediction of Chaotic Dynamical Systems using Machine Learning

#### November 29, 2021

**Prof. Edward Ott** will discuss the use of machine learning for predicting the future evolution of dynamical systems, including systems that are very large, complex, and chaotic. He will explain reservoir computing, the basic machine learning method used in this talk. Following that, he will illustrate prediction on simple systems, hybrid prediction combining machine learning with physical knowledge, and a parallel configuration for treating large spatiotemporally chaotic systems. Illustrations and recent progress on applications to terrestrial weather and climate prediction will be presented.

Professor Ott’s current research is on the basic theory and applications of nonlinear dynamics. Some of his current research projects are in wave chaos, dynamics on large interconnected networks, chaotic dynamics of fluids, and weather prediction. Professor Ott is a fellow of the American Physical Society, the Institute of Electrical and Electronics Engineers, and the Society for Industrial and Applied Mathematics (SIAM). He is the recipient of the APS Julius Edgar Lilienfield Prize for 2014.

Photo credits: https://www.ae-info.org/ae/Member/Ott_Edward

**Prof. Kazuyuki Aihara**, U. Tokyo

### Data Analysis on Critical Transitions in Complex Systems and its Application to Early Precision Medicine

#### October 25, 2021

**Prof. Kazuyuki Aihara** reviewed his group’s recent studies on DNB (Dynamical Network Biomarkers) that provide early warning signals of imminent bifurcation from a healthy state to a disease state through a pre-disease state. He also explained the possible application of DNB for early precision medicine.

Kazuyuki Aihara received a B.E. degree in electrical engineering and Ph.D. degree in electronic engineering from the University of Tokyo (UTokyo), Tokyo, Japan, in 1977 and 1982, respectively. He led the ERATO (Exploratory Research for Advanced Technology) Aihara Complexity Modelling project by JST (Japan Science and Technology Agency) from 2003 to 2008 and the FIRST Innovative Mathematical Modelling project by JSPS (Japan Society for the Promotion of Science) through the FIRST (Funding Program for World-Leading Innovative R&D Science and Technology) program from 2010 to 2014 designed by CSTP (Council for Science and Technology Policy). Currently, he is University Professor and Professor Emeritus of UTokyo, Deputy Director at the International Research Center for Neurointelligence (IRCN) at UTokyo, and Project Manager of the Moonshot project by the cabinet office of the Japanese government on “Comprehensive Mathematical Understanding of the Complex Control System between Organs and Challenge for Ultra-Early Precision Medicine.”

Photo credits: https://ircn.jp/en/mission/people/kazuyuki_aihara

**Prof. Jürgen Kurths**, PIK Germany

### Exploring Predictability of Extreme Climate Events via a Complex Network Approach

#### September 27, 2021

Earth is a complex system whose dynamics involve innumerous interactions and multiple feedbacks. This makes predictions and risk analysis of very strong, and sometimes extreme events such as floods, landslides, heatwaves, earthquakes, etc., a challenging task. Here, I will introduce a recently developed approach via complex networks to analyze strong climate events. This leads to an inverse problem: Is there a backbone-like structure underlying the climate system? Towards this, we propose a method to reconstruct and analyze a complex network from observational and reanalysis data. This approach enables us to uncover relations to global and regional circulation patterns in oceans and atmosphere, which leads to substantially better predictions of high-impact phenomena, in particular of the Indian Summer Monsoon, El Nino events, droughts in the central Amazon, extreme rainfall in the Eastern Central Andes, and the Pacific decadal oscillation. I argue that network-based approaches can significantly complement numerical modeling for better predictions of the extreme weather events and lead to a better understanding of meteorological data.

**Prof. Jürgen Kurths** is Senior Advisor at Research Department for “Complexity Science” at Potsdam Institute for Climate Impact Research (PIK) as well as Professor and Senior Advisor at Humboldt University Berlin.

Photo credits: https://www.pik-potsdam.de/members/kurths/homepage