AbstractsPlenary SpeakerSpeaker: Antoine Chaillet Affiliation: L2S - CentraleSupélec
- Université Paris-Saclay Time: 10:00-10:50 Title: Recent Results and Open Questions for the Stability and Robustness of Nonlinear Time-Delay Systems Abstract: The input-to-state stability (ISS) property offers an interesting framework to study both stability and robustness of nonlinear systems. While this concept is now well developed in a finite-dimensional context, several important questions remain open when working with infinite-dimensional systems. This presentation will focus on a particular class of such systems, namely time-delay systems. Based on our recent survey paper, we will review fundamental results to study ISS of time-delay systems, particularly through the tool of Lyapunov-Krasovskii functionals (LKF). We will also report some recent results related to the possibility of deriving stability properties based on a LKF whose dissipation is merely in terms of the current value of the solution's norm (point-wise dissipation). We will also list a series of open questions in the field and describe the partial answers obtained so far. Bio: Antoine Chaillet was born in Douai, France, in 1979. In 2002, he received his B.Sc. degree from ESIEE Amiens, France, and his M.Sc. degree in Control Engineering from Univ. Paris Sud 11 in 2003. In July 2006, he received his Ph.D. degree cum laude in Control Theory from Univ. Paris Sud 11-L2S. In 2004, A. Chaillet was recipient of a Marie-Curie Scholarship to visit Università degli Studi di Firenze, Italy. In 2006–2007, he served as a post-doc fellow at Centro di Ricerca Piaggio, Pisa, Italy. From 2007 to 2016, he served as an associate professor at L2S-Univ. Paris Sud 11-Supélec-EECI. He is now full professor at CentraleSupélec and former junior member of Institut Universitaire de France. His research interests include stability analysis and stabilization of nonlinear systems, time-delay systems, and control theory for neuroscience. He is the author of around 100 peer-reviewed publications on these topics. Invited SpeakersSpeaker: Fatihcan Atay Affiliation: Bilkent University Time: 11:20-11:40 Title: Anticipatory Dynamics in Networks of Nonlinear Systems Abstract: We consider networks of coupled nonlinear systems where the individual units try to anticipate the states of their neighbors and align their states accordingly. We present a model of anticipation that uses past information to predict the future, and hence introduces a memory term in the form of a time delay. We study the stability of synchronized states in the presence of such delays. We show that, depending on the delay value, anticipation can facilitate synchronization or cause instabilities that cause the network to move towards a rich spectrum of dynamical patterns. Speaker: Ali Demirci Co-Authors: Ayşe Peker-Dobie, Sevgi Harman Affiliation: Istanbul Technical
University Time: 11:40-12:00 Title: Nonlinear Dynamics of Polarization in Social Systems Abstract: Polarization in social systems is a complex collective phenomenon arising from nonlinear interactions among individuals exposed to competing information streams. In this study, we model polarization as a nonlinear dynamical system where individuals transition between positive, negative, and mixed-emotion communicative states under the influence of peers and media. The framework extends epidemic-like compartmental models by incorporating time-dependent engagement and nonlinear influence asymmetry, allowing the system to exhibit diverse dynamical behaviors such as multistability, oscillations, and critical transitions. Our analysis shows that engagement asymmetry—differences in how strongly polarized groups participate in discourse—can sustain polarization even when a large fraction of the population remains moderate. Increasing overall engagement may, counterintuitively, stabilize polarized attractors, while controlled disengagement or curiosity-driven diffusion may restore collective moderation. The resulting bifurcation landscape highlights how external interventions, if improperly timed or scaled, can amplify rather than suppress polarization. By linking control parameters to real-world mechanisms such as media exposure and algorithmic filtering, the model provides a quantitative lens for examining how societies shift between fragmented and cohesive states. The nonlinear perspective thus reveals that polarization control depends less on reducing influence intensity and more on restructuring the feedback topology governing opinion exchange. This framework bridges mathematical modeling and socio-cognitive dynamics, offering new insight into how public discourse may be guided toward stability and inclusivity. Speaker: Taylan Şengül Affiliation: Marmara University Time: 14:00-14:20 Title: Dynamic Transitions in the Perspective of Symmetry Abstract: This talk will be about the dynamic transitions of some general reaction diffusion systems. The dynamic transitions occur when a state loses its stability which gives rise to new stable states. The symmetries possessed by these systems and the new states that arise are inherently related. In this talk I will describe the relation between dynamic transitions and the underlying symmetry. Speaker: Gökhan Göksu Co-Authors: Mertcan Gürler, Antoine Chaillet Affiliation: Yıldız
Technical University Time: 14:20-14:40 Title: Lyapunov-Krasovskii Conditions for Strong Integral Input-To-State Stable in Time-Delay Systems Abstract: In this talk, we present Lyapunov-Krasovskii theorems for strong integral input-to-state stable time-delay systems, showing that a dissipation rate involving the Lyapunov-Krasovskii functional guarantees strong iISS under a specific threshold. A unified framework combining ISS for small inputs and forward completeness further characterizes strong iISS. An example illustrates how a time-delay system with both instantaneous and historical state norms satisfies the strong iISS property. Speaker: Derya Sekman Affiliation: Yıldız
Technical University Time: 14:40-15:00 Title: Approach of Fixed Point Theory to Chaos Control: Iterative Stabilization Mechanisms and Computational Applications Abstract: This study
presents a comprehensive framework examining the role of fixed point iteration
theory in the analysis and control of chaotic behaviors in nonlinear discrete
dynamical systems. To achieve chaos suppression, various iterative control
mechanisms, such as Mann, Ishikawa, Noor, Multistep, S, Picard-S, Thakur, Karakaya, Normal-S, M and multivalued fixed point
iterations are theoretically formulated, and their stability conditions are
analytically established. By employing Gâteaux and Fréchet derivatives in Banach
spaces, derivative-based control intervals are derived to identify stability
and instability regions depending on system parameters, with the validity of
these regions verified through Lyapunov exponent
computations. Extending beyond classical single-valued models, one-step
feedback mechanisms for multivalued discrete dynamical systems are proposed,
and their stabilizing effects under contraction conditions are investigated.
Computer simulations performed on logistic and tent-type chaotic maps confirm
that the proposed iterative control mechanisms transform chaotic trajectories
into stable regimes. Furthermore, applications to tent-based electronic circuit
models and the traffic control model demonstrate the effectiveness of the
developed methods in both engineering and system dynamics contexts.
Collectively, this work bridges the theoretical gap between abstract fixed
point theory and practical chaos control, offering an integrated framework that
connects mathematical analysis with real-world engineering implementations. Speaker: Cihangir Özemir Co-Authors: Şeyma Gönül, Yasin Hasanoğlu Affiliation: Istanbul Technical
University Time: 15:30-15:50 Title: Lie Algebras and
Solutions of Davey-Stewartson Type Systems Abstract: The Davey-Stewartson (DS) system was first introduced in the context of free surface waves subject to both gravitational and surface tension effects. Since then, various forms of the DS system have been derived in many different fields, including solid mechanics, optics, electromagnetic waves and plasma physics. In this work, we present a Lie symmetry approach to the analysis of
DS-type systems with quintic nonlinearities, as well
as a generalized DS system involving three interacting wave components. The
invariance algebras turn out to be infinite-dimensional Lie algebras, allowing
reductions to lower-dimensional equations. We shall also mention analytic
solutions, stability of traveling-waves and a result on global existence of
solutions. Speaker: Ilmar Gahramanov Affiliation: Boğaziçi
University Time: 15:50-16:10 Title: Combinatorial
Structures in a Dubrovin–Novikov
Type System Abstract: We study a
special class of Hamiltonian systems belonging to the family of equations of
hydrodynamic type, originally introduced by Dubrovin
and Novikov. The system arises as a particular
generalization of the exact renormalization group flow in matrix scalar field
theory. By analyzing its first integrals, we uncover a remarkably structured
pattern governed by the coefficients of Motzkin
polynomials. Each integral of motion can be naturally associated with a
distinct path on the unit lattice, revealing an elegant combinatorial
interpretation of the system’s conservation laws. Poster SessionsPresenter: İsmail Önder Affiliation: Yıldız Technical University Title: Soliton Solution of Some Partial Differential Equations, Phase Diagrams, Chaotic, Bifurcation, Sensitivity and Stability Analysis Presenter: Mustafa Mullahasanoğlu Affiliation: Boğaziçi University Title: From Supersymmetric Quantum Mechanics to Memory Effects in Gravitational Waves Presenter: Nazira Murat Co-Author: Fatihcan Atay Affiliation: Bilkent University Title: Synchronization in Networks of Anticipatory Agents |