2025

Ludovico Minati, Vitrice Ruben Folifack Signing, Léandre Kamdjeu Kengne, Manyu Zhao, Pedro Antonio Valdes-Sosa, Hiroyuki Ito, Xu Zhang, Leonardo Ricci & Christophe Letellier
A three-dimensional non-autonomous conservative chaotic system based on cross-phase-coupled oscillators : Theoretical analysis and electronic realization
Chaos, Solitons & Fractals, 200, 116877, 2025. Online

• Abstract
  This study concerns a conservative, non-autonomous chaotic system composed of three ordinary differential equations, each of which solely comprises a sine function of time and cross-coupling terms. While devoid of an attractive invariant set, the system is not Hamiltonian. It was recently introduced as an abstraction of a chaotic oscillator circuit based on CMOS inverter rings. Moreover, it has aspects of structural resemblance with particular configurations of the Kuramoto model, as well as coupled Josephson junctions, and can be intended to represent a high-order interaction. Numerical simulations, based on reformulations as an equivalent autonomous system, reveal two distinct chaotic regimes under the assumption of homogeneous or heterogeneous harmonic excitation. Under homogeneous excitation, the trajectories remain bounded and are organized into a chaotic sea interspersed with quasi-periodic islands. In the heterogeneous case, labyrinth chaos is generated, characterized by aperiodic wandering akin to a perturbed Wiener process and reminiscent of the behavior of the Thomas system. The trajectory spread underlying the transition between bounded and unbounded behaviors is controlled by the cross-coupling strength, and, in the presence of growing dissipation, the orbits are increasingly constrained. A realization based on transfer functions and voltage- controlled oscillators is also presented, and was simulated both at block level and in terms of a realistic electronic circuit. A minimalist experimental implementation using commonplace 555-type timer integrated circuits was constructed and found to reproduce salient aspects of the dynamics. Besides the distinguishing structural features of the equation system and its dynamics,

Christophe Letellier, Manyu Zhao & Pierre Bénard
Influence of eolian farms on climate dynamics : A simple model point of view
Chaos, Solitons & Fractals, 199, 116883, 2025. Online

• Abstract
  With the amazing development of wind energy, it is worthy to investigate how the energy, pumped in the wind, can affect the atmospheric circulation and whether it could contribute to climate change. We therefore considered this problem with a simple physically motivated model for the interaction between wind and the Pacific Ocean as proposed by Vallis (1986). A realistic pumping function, corresponding to the energy harvested by wind turbine, is inserted and its influence in the initial ‘‘climate’’ dynamics is characterized using a topological approach. Results suggest that wind energy is not so ‘‘abundant and inexhaustible’’. This work investigates the possible effect of wind turbines on climate using a very simple climate model. With the major development of wind farms, the fraction of wind energy pumped may become significant, at least sufficiently to destabilize some main atmosphere circulations as El-Niño-Southern Oscillation (ENSO). This issue is addressed by using a realistic pumping function for wind turbines coupled to a simple model for the ENSO. This preliminary work suggests that wind turbines could indeed contribute to climate change.

I. Leyva, Juan A. Almendral, Christophe Letellier & Irene Sendiña-Nadal
Local predictors of explosive synchronization with ordinal methods
Entropy, 27, 113, 2025. Online

• Abstract
  We propose using the ordinal pattern transition (OPT) entropy measured at sentinel central nodes as a potential predictor of explosive transitions to synchronization in networks of various dynamical systems with increasing complexity. Our results demonstrate that the OPT entropic measure surpasses traditional early warning signal measures and could be valuable to the tools available for predicting critical transitions. In particular, we investigate networks of diffusively coupled phase oscillators and chaotic Rössler systems. As maps, we consider a neural network of Chialvo maps coupled in star and scale-free configurations. Furthermore, we apply this measure to time series data obtained from a network of electronic circuits operating in the chaotic regime.

Juan Cruz Bonel, Nicolás Bodnariuk, Gisela D. Charó, Christophe Letellier, Christophe Guinet, Martín Saraceno & Denisse Sciamarella
Templex for Lagrangian dynamics in the Southwestern Atlantic
Chaos, 35, 103137, 2025. Online

• Abstract
  This work presents the first application of the templex approach to observational datasets, using Lagrangian trajectories obtained from satellite altimetry in the ocean. The templex is a recent topological construct that extends classical ideas from template theory to higher-dimensional systems. Unlike other methods in topological data analysis, which lack flow information, a templex encodes both the structure of phase space through a branched manifold analysis through homologies cell complex and the organization of flow cycles upon it through a directed graph defined on its highest-dimensional cells. As shown in earlier works, the description of flows in phase space indirectly enables a description of fluid flows in physical space, since particles sharing the same dynamics are known to move coherently. Particle sets in the Southwestern Atlantic Ocean are analyzed, revealing that the Lagrangian finite-time dynamics in this region can be related to those produced by a nonautonomous meandering jet model. We distinguished non-mixing (regular) islands from the chaotic sea. The results are also compared to those obtained from metric methods describing material transport in fluid flows and to the spatial organization of chlorophyll-a concentration. The seasonal variability of chaotic dynamics is also discussed.

Christophe Letellier, Léandre Kamdjeu Kengne, Manyu Zhao & Ludovico Minati
To be an extreme event or not : That is the question
Chaos, 35, 073119, 2025. Online

• Abstract
  Considering the lack of consensus for defining extreme events, we propose to revisit their definition. Our definition is based on the topological characterization of nominal dynamics, that is, hereafter, distinguished from extreme events with the help of two thresholds, one for the oscillation amplitude and one for the return time between two successive intersections with a surface of section. Two examples are investigated : one 3D jerk system and a 9D model for Rayleigh–Bénard convection. In the first example, the tipping point between small- and large-amplitude oscillations is topologically identified. The possibility of predicting the latter is investigated.

• Katherine De Lange, Distinguishing extreme events from nominal chaos, Scilight, 2025, 291104, 2025. Online

Christophe Letellier, Ludovico Minati, Jean-Pierre Barbot, Irene Sendiña-Nadal & I. Leyva
Flatness-based control for generalized synchronization of chaotic systems with large dissipation and dimension mismatch
Chaos, 35, 093119, 2025. Online

• Abstract
  A flat control law is based on the structural analysis of a controlled system, allowing optimal placement of sensors and actuators. Once designed, any desired dynamics can be imposed onto the system. When the target dynamics comes from a system structurally different from the controlled one, generalized synchronization can be achieved, provided the control gain is sufficiently large. As the gain increases, various relationships emerge between the drive and response systems, depending on differences in their dimensions and dissipation rates. The principal contribution of this work lies in the exploration of drive-response system pairs with varying dimensions (ranging from 2 to 4) and dissipation levels, including combinations of dissipative and conservative systems. We identify several types of generalized synchronization, using a classification based on the thickness of the resulting Lissajous curves and the lack of conjugacy between the first-return maps of the drive and response systems.

Christophe Letellier · Irene Sendiña-Nadal, Ludovico Minati & Jean-Pierre Barbot
Flat control law for diffusively \(y\)-coupled Rössler systems
Nonlinear Dynamics, 113, 16511–16529, 2025. Online

• Abstract
  Controlling dynamical systems, specially high dimensional dynamical networks, is of primary interest. Such a problem is intrinsically related to analyzing the observability of the corresponding state space from measurements, as well as its dual aspect of controllability. An additional constraint can be added by requiring the system to be flat, meaning that its state and actuating signal can be expressed in terms of the measurements and a finite number of its derivatives. Starting from the placement of sensors providing global observability, we address the dual problem of placing the actuators allowing global controllability, and of designing a flat input. Since global observability of a network of y-coupled Rössler systems can be reduced to the observability of each pair of nodes, a step before controlling a network is to design a flat control law for a pair of diffusively y-coupled Rössler systems. It is shown that such a system is flat when a differential delay is inserted.

Zeric Tabekoueng Njitacke, Joakim Vianney Ngamsa Tegnitsap, Manyu Zhao, Chiara Barà, Théophile Fonzin Fozin, Jan Awrejcewicz, Natsue Yoshimura, Pedro A. Valdes-Sosa, Christophe Letellier & Ludovico Minati
Chaotic dynamics, topological analysis and flat analog electronic control by physiological signals of a neurally-inspired system
Chinese Journal of Physics, 96, 20–52, 2025. Online

• Abstract
  A novel abstract bicompartmental neural model based on a cubic nonlinearity, consisting of introducing a Josephson junction as a coupling element, is presented. Through numerical simulations and experimental measurements involving an analog electronic circuit, it is found that the system can generate a double-scroll chaotic attractor endowed with a remarkably complex topology. This is accompanied by diversification of the spectral signature across its four variables and multistability. An analysis of the global observability and controllability is conducted, leading to the synthesis of a flat controller that can steer the dynamics towards those of structurally different entities, as exemplified by a modified Lorenz system. The first analog realization of flat control is then introduced. The possibility of low-latency and high-accuracy manipulation of the dynamics is demonstrated by considering the challenging case of tracking extraneous external signals, namely, physiological recordings indexing autonomic and central nervous system activity. Besides showing the flexibility and adaptability of the approach, the controller enables the concomitant generation of multiple additional signals with spectrogram features compared to the individual inputs, offering a promising substrate for future applications in physical time series data augmentation.