CyberSec Research

The study of experimental data is a relevant task in several physical, chemical and biological applications. In particular, the analysis of chaotic dynamics in cardiac systems is crucial as it can be related to some pathological arrhythmias. When working with short and noisy experimental time series, some standard techniques for chaos detection cannot provide reliable results because of such data characteristics. Moreover, when small datasets are available, Deep Learning techniques cannot be applied directly (that is, using part of the data to train the network, and using the trained network to analyze the remaining dataset). To avoid all these limitations, we propose an automatic algorithm that combines Deep Learning and some selection strategies based on a mathematical model of the same nature of the experimental data. To show its performance, we test it with experimental data obtained from ex-vivo frog heart experiments, obtaining highly accurate results.

As electronic computing approaches its performance limits, photonic accelerators have emerged as promising alternatives. Photonic accelerators exploiting semiconductor-laser synchronization have been studied for decision-making. While conventional cross-correlation methods are computationally intensive and memory demanding, we propose a frequency-based approach using optical frequency differences. Simulations and experiments confirm that this method achieves decision making with reduced cost and memory requirements.

This paper investigates the dynamics of quantum analogs of classical impact oscillators to explore how complex nonlinear behaviors manifest in quantum systems. While classical impact oscillators exhibit chaos and bifurcations, quantum systems, governed by linear equations, appear to forbid such dynamics. Through simulations of unforced, forced, and dissipative quantum oscillators, we uncover quasiperiodicity, strange nonchaotic dynamics, and even chaos in the presence of dissipation. Using entropy time series, Fourier spectra, OTOCs, Lyapunov analysis, and the 0-1 test, we demonstrate that quantum systems can exhibit rich dynamical signatures analogous to classical nonlinear systems, bridging quantum mechanics and chaos theory.

Classical methods of sound absorption present fundamental limits that can be overcome by using nonlinear effects. Thin clamped plates have been identified as strongly nonlinear elements, capable of transferring the acoustic power of an incident air-borne wave towards higher frequencies. Here, we experimentally show that these plates exhibit different vibrational nonlinear behaviors depending on the amplitude and frequency of the excitation signal. The lowest excitation levels achieved lead to harmonic generation in a weakly nonlinear regime, while higher levels produce quasi-periodic and chaotic regimes. Since these nonlinear vibration regimes govern the acoustic frequency-up conversion process, we investigate the influence of relevant physical and geometrical parameters on the emergence of these nonlinear regimes. A parametric study on plates of different thicknesses reveals that the frequency-up conversion effect is mostly guided by the resonance of the plate at its first eigenfrequency, which depends not only on its thickness but also on a static tension introduced by the clamping. Finally, a design proposition involving multiple plates with different properties is presented in order to reach a broadband frequency-up conversion.

The theory of embedding and generalized synchronization in reservoir computing has recently been developed. Under ideal conditions, reservoir computing exhibits generalized synchronization during the learning process. These insights form a rigorous basis for understanding reservoir computing ability to reconstruct and predict complex dynamics. In this study, we clarified the dynamical system structures of generalized synchronization and embedding by comparing the Lyapunov exponents of a high dimensional neural network within the reservoir computing model with those in actual systems. Furthermore, we numerically calculated the Lyapunov exponents restricted to the tangent space of the inertial manifold in a high dimensional neural network. Our results demonstrate that all Lyapunov exponents of the actual dynamics, including negative ones, are successfully identified.

Understanding the dynamical structure of cislunar space beyond geosynchronous orbit is critical for both lunar exploration and for high-Earth-orbiting trajectories. In this study, we investigate the role of mean-motion resonances and their associated heteroclinic connections in enabling natural semi-major axis transport in the Earth-Moon system. Working within the planar circular restricted three-body problem, we compute and analyze families of periodic orbits associated with the interior 4:1, 3:1, and 2:1 lunar resonances. These families exhibit a rich bifurcation structure, including transitions between prograde and retrograde branches and connections through collision orbits. We construct stable and unstable manifolds of the unstable resonant orbits using a perigee-based Poincar\'e map, and identify heteroclinic connections - both between resonant orbits and with lunar $L_1$ libration-point orbits - across a range of Jacobi constant values. Using a new generalized distance metric to quantify the closeness between trajectories, we establish operational times-of-flight for such heteroclinic-type orbit-to-orbit transfers. These connections reveal ballistic, zero-$\Delta v$ pathways that achieve major orbit changes within reasonable times-of-flight, thus defining a network of accessible semi-major axes. Our results provide a new dynamical framework for long-term spacecraft evolution and cislunar mission design, particularly in regimes where lunar gravity strongly perturbs high Earth orbits.

We investigate the boundary separating regular and chaotic dynamics in the generalized Chirikov map, an extension of the standard map with phase-shifted secondary kicks. Lyapunov maps were computed across the parameter space (K, K{\alpha}, {\tau} ) and used to train a convolutional neural network (ResNet18) for binary classification of dynamical regimes. The model reproduces the known critical parameter for the onset of global chaos in the standard map and identifies two-dimensional boundaries in the generalized map for varying phase shifts {\tau} . The results reveal systematic deformation of the boundary as {\tau} increases, highlighting the sensitivity of the system to phase modulation and demonstrating the ability of machine learning to extract interpretable features of complex Hamiltonian dynamics. This framework allows precise characterization of stability boundaries in nontrivial nonlinear systems.

This paper explores a novel connection between a thermodynamic and a dynamical systems perspective on emergent dynamical order. We provide evidence for a conjecture that Hamiltonian systems with mixed chaos spontaneously find regular behavior when minimally coupled to a thermal bath at sufficiently low temperature. Numerical evidence across a diverse set of five dynamical systems supports this conjecture, and allows us to quantify corollaries about the organization timescales and disruption of order at higher temperatures. Balancing the damping-induced phase-space contraction against thermal exploration, we are able to predict the transition temperatures in terms of the relaxation timescales, indicating a novel nonequilibrium fluctuation-dissipation relation, and formally connecting the thermodynamic and dynamical systems views. Our findings suggest that for a wide range of real-world systems, coupling to a cold thermal bath leads to emergence of robust, non-trivial dynamical order, rather than a mere reduction of motion as in equilibrium.

This paper investigates the symmetry properties of basins of attraction and their boundaries in equivariant dynamical systems. While the symmetry groups of compact attractors are well understood, the corresponding analysis for non-compact basins and their boundaries has remained underdeveloped. We establish a rigorous theoretical framework demonstrating the hierarchical inclusion of a chain of symmetry groups, showing that boundary symmetries can strictly exceed those of attractors and their basins. To determine admissible symmetry groups of basin boundaries, we propose three complementary approaches: (i) thickening transfer, which connects admissibility results from compact attractors to basins; (ii) algebraic constraints, which exploit the closed nature of boundaries to impose structural restrictions; and (iii) connectivity and flow analysis, which analyzes how the system's dynamics permute states. Numerical experiments on the Thomas system confirm these theoretical results, illustrating that cyclic group actions permute basins while preserving their common boundary, whereas central inversion leaves both basins and boundaries invariant. These findings reveal that basin boundaries often exhibit higher symmetry than the attractors they separate, providing new insights into the geometry of multistable systems and suggesting broader applications to physical and biological models where basin structure determines stability and predictability.

Recently, a concept of deterministic and stochastic turbulence has been introduced based on experiments with a boundary layer. A deterministic property means that identical random perturbations at the inlet lead to identical patterns downstream; during this stage, the non-identical, stochastic component grows and eventually dominates the flow further downstream. We argue that these properties can be explained by exploring the concept of convective space-time chaos, where secondary perturbations on top of a chaotic state grow but move away in the laboratory reference frame. We illustrate this with two simple models of convective space-time chaos, one is a partial differential equation describing waves on a film flowing down a plate, and the other is a set of unidirectionally coupled ordinary differential equations. To prove convective space-time chaos, we calculate the profiles of the convective Lyapunov exponent. The repeatability of the turbulent field in different identical experimental runs corresponds to the reliability of stable dynamical systems in response to random forcing. The onset of the stochastic component is quantified with the spatial Lyapunov exponent. We demonstrate how an effective randomization of the field is observed when the driving is quasiperiodic. Furthermore, we discuss space-time duality, which links sensitivity to boundary conditions in the convective space-time chaos to the usual sensitivity to initial conditions in a standard chaotic regime.

We demonstrate the deterministic coherence and anti-coherence resonance phenomena in two coupled identical chaotic Lorenz oscillators. Both effects are found to occur simultaneously when varying the coupling strength. In particular, the occurrence of deterministic coherence resonance is revealed by analysing time realizations $x(t)$ and $y(t)$ of both oscillators, whereas the anti-coherence resonance is identified when considering oscillations $z(t)$ at the same parameter values. Both resonances are observed when the coupling strength does not exceed a threshold value corresponding to complete synchronization of the interacting chaotic oscillators. In such a case, the coupled oscillators exhibit the hyperchaotic dynamics associated with the on-off intermittency. The highlighted effects are studied in numerical simulations and confirmed in physical experiments, showing an excellent correspondence and disclosing thereby the robustness of the observed phenomena.

The dynamical symmetry breaking associated with the existence and non-existence of breather solutions is studied. Here, nonlinear hyperbolic evolution equations are calculated using a high-precision numerical scheme. %%% First, for clarifying the dynamical symmetry breaking, it is necessary to use a sufficiently high-precision scheme in the time-dependent framework. Second, the error of numerical calculations is generally more easily accumulated for calculating hyperbolic equations rather than parabolic equations. Third, numerical calculations become easily unstable for nonlinear cases. Our strategy for the high-precision and stable scheme is to implement the implicit Runge-Kutta method for time, and the Fourier spectral decomposition for space. %%% In this paper, focusing on the breather solutions, the relationship between the velocity, mass, and the amplitude of the perturbation is clarified. As a result, the conditions for transitioning from one state to another are clarified.

Several definitions of phase have been proposed for stochastic oscillators, among which the mean-return-time phase and the stochastic asymptotic phase have drawn particular attention. Quantitative comparisons between these two definitions have been done in previous studies, but physical interpretations of such a relation are still missing. In this work, we illustrate this relation using the geometric phase, which is an essential concept in both classical and quantum mechanics. We use properties of probability currents and the generalized Doob's h-transform to explain how the geometric phase arises in stochastic oscillators. Such an analogy is also reminiscent of the noise-induced phase shift in oscillatory systems with deterministic perturbation, allowing us to compare the phase responses in deterministic and stochastic oscillators. The resulting framework unifies these distinct phase definitions and reveals that their difference is governed by a geometric drift term analogous to curvature. This interpretation bridges spectral theory, stochastic dynamics, and geometric phase, and provides new insight into how noise reshapes oscillatory behavior. Our results suggest broader applications of geometric-phase concepts to coupled stochastic oscillators and neural models.

We obtain and investigate theoretically a broad family of stable and unstable time-periodic orbits-oscillating Turing rolls (OTR)-in the Lugiato-Lefever model of optical cavities. Using the dynamical systems tools developed in fluid dynamics, we access the OTR solution branches in parameter space and elucidate their bifurcation structure. By tracking these exact invariant solutions deeply into the chaotic region of the modulation instability, we connect the main dynamical regimes of the Lugiato-Lefever model: continuous waves, Turing rolls, solitons, and breathers, which completes the classical phase diagram of the optical cavity. We then demonstrate that the OTR periodic orbits play a fundamental role as elementary building blocks in the regime of the intracavity field transition from stable Turing rolls to fully developed turbulent regimes. Depending on the cavity size, we observe that the chaotic intracavity field driven by modulation instability displays either spatiotemporal or purely temporal intermittancy between chaotic dynamics and different families of the OTR solutions, exhibiting locally the distinctive wave patterns and large amplitude peaks. This opens avenues for a theoretical description of optical turbulence within the dynamical systems framework.

The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation entropy. The probability density function associated with the particle positions evolves to a Gaussian distribution, and the second moment follows a power-law dependence on time, indicative of diffusive behavior. The results emphasize that deterministic systems with complex geometries or nonlinearities can generate behavior that is statistically indistinguishable from random. Several problems are suggested to extend the analysis.

We study in detail the critical points of Bohmian flow, both in the inertial frame of reference (Y-points) and in the frames centered at the moving nodal points of the guiding wavefunction (X-points), and analyze their role in the onset of chaos in a system of two entangled qubits. We find the distances between these critical points and a moving Bohmian particle at varying levels of entanglement, with particular emphasis on the times at which chaos arises. Then, we find why some trajectories are ordered, without any chaos. Finally, we examine numerically how the Lyapunov Characteristic Number (LCN ) depends on the degree of quantum entanglement. Our results indicate that increasing entanglement reduces the convergence time of the finite-time LCN of the chaotic trajectories toward its final positive value.

We study in detail the form of the orbits in integrable generalized H\'enon-Heiles systems with Hamiltonians of the form $H = \frac{1}{2}(\dot{x}^2 + Ax^2 + \dot{y}^2 + By^2) + \epsilon(xy^2 + \alpha x^3).$ In particular, we focus on the invariant curves on Poincar\'e surfaces of section ($ y = 0$) and the corresponding orbits on the $x-y$ plane. We provide a detailed analysis of the transition from bounded to escaping orbits in each integrable system case, highlighting the mechanism behind the escape to infinity. Then, we investigate the form of the non-escaping orbits, conducting a comparative analysis across various integrable cases and physical parameters.

We present a deep learning emulator for stochastic and chaotic spatio-temporal systems, explicitly conditioned on the parameter values of the underlying partial differential equations (PDEs). Our approach involves pre-training the model on a single parameter domain, followed by fine-tuning on a smaller, yet diverse dataset, enabling generalisation across a broad range of parameter values. By incorporating local attention mechanisms, the network is capable of handling varying domain sizes and resolutions. This enables computationally efficient pre-training on smaller domains while requiring only a small additional dataset to learn how to generalise to larger domain sizes. We demonstrate the model's capabilities on the chaotic Kuramoto-Sivashinsky equation and stochastically-forced beta-plane turbulence, showcasing its ability to capture phenomena at interpolated parameter values. The emulator provides significant computational speed-ups over conventional numerical integration, facilitating efficient exploration of parameter space, while a probabilistic variant of the emulator provides uncertainty quantification, allowing for the statistical study of rare events.