Properties Of Dynamical Systems Research Articles

Gesture recognition with Brownian reservoir computing using geometrically confined skyrmion dynamics

Physical reservoir computing leverages the dynamical properties of complex physical systems to process information efficiently, significantly reducing training efforts and energy consumption. Magnetic skyrmions, topological spin textures, are promising candidates for reservoir computing systems due to their enhanced stability, non-linear interactions and low-power manipulation. Traditional spin-based reservoir computing has been limited to quasi-static detection or real-world data must be rescaled to the intrinsic timescale of the reservoir. We address this challenge by time-multiplexed skyrmion reservoir computing, that allows for aligning the reservoir’s intrinsic timescales to real-world temporal patterns. Using millisecond-scale hand gestures recorded with Range-Doppler radar, we feed voltage excitations directly into our device and detect the skyrmion trajectory evolution. This method scales down to the nanometer level and demonstrates competitive or superior performance compared to energy-intensive software-based neural networks. Our hardware approach’s key advantage is its ability to integrate sensor data in real-time without temporal rescaling, enabling numerous applications.

Relaxation rate of ModMax–de Sitter black holes perturbed by massless neutral scalar fields

In this study, we investigate the behavior of ModMax-de Sitter black holes when perturbed by massless neutral scalar fields. Specifically, we analyze how the relaxation time, defined as the inverse of the fundamental imaginary frequency, varies with respect to two key parameters: the cosmological constant and the nonlinear parameter characterizing the ModMax theory. We explore scenarios both with and without a cosmological constant, focusing on the static charged ModMax black hole configuration. Our results reveal dependencies between the relaxation time and the nonlinear parameter, shedding light on the dynamical properties of these black hole systems. We also show the validity of WKB approximation under consideration.

A Four-Dimensional No-Equilibrium Chaotic System with Multi-Scroll Chaotic Hidden Attractors and its Application in Image Encryption

Abstract In recent years, constructing hidden attractors with multi-scroll has become a key discussion point in the research and application fields of chaos science. In this paper, with the existing four-dimensional (4D) chaotic system as the base, a new four-dimensional chaotic system featuring significant characteristics of multi-scroll hidden attractors is constructed by adding a nonlinear function. Comprehensive studies including theoretical analyses and numerical simulations have been carried out on the dynamic properties of the new chaotic system, and all the results show that this system exhibits extremely complex chaotic behaviours and excellent unpredictability, which has great value in image encryption. Therefore, an image encryption scheme based on the new chaotic system is proposed, which cleverly integrates the new scrambling algorithm based on parity coordinate transformation and the new rotational diffusion algorithm. And the effectiveness of this encryption algorithm has been thoroughly analyzed and tested. The results based on the experiments show that this encryption algorithm exhibits significant advantages in performance, which can greatly enhance the security of images during encryption and transmission.

Contrasting alterations in brain chemistry in a crustacean intermediate host of two acanthocephalan parasites

The dynamic properties of neural systems throughout life can be hijacked by so-called manipulative parasites. This study investigated changes in the brain chemistry of the amphipod Gammarus fossarum in response to infection with two trophically-transmitted helminth parasites known to induce distinct behavioral alterations: the bird acanthocephalan Polymorphus minutus and the fish acanthocephalan Pomphorhynchus tereticollis. We quantified brain antioxidant capacity as a common marker of homeostasis and neuroprotection, and brain total protein, on 72 pools of six brains. We analyzed the concentration of serotonin (5HT), dopamine (DA) and tyramine in 52 pools of six brains, by using ultrafast high performance liquid chromatography with electrochemical detection (UHPLC-ECD). Brain total protein concentration scaled hypo-allometrically to dry body weight, and was increased in infected gammarids compared to uninfected ones. The brain of gammarids infected with P. minutus had significantly lower total antioxidant capacity relative to total proteins. Infection with P. tereticollis impacted DA level compared to uninfected ones, and in opposite direction between spring and summer. Brain 5HT level was higher in summer compared to spring independently of infection status, and was decreased by infection after correcting for brain total protein concentration estimated from dry whole-body weight. The potential implication of 5HT/DA balance in parasite manipulation, as a major modulator of the reward-punishment axis, is discussed. Taken together, these findings highlight the need to consider both brain homeostatic and/or structural changes (antioxidant and total protein content) together with neurotransmission balance and flexibility, in studies investigating the impact of parasites on brain and behavior.

Kylin-V: An open-source package calculating the dynamic and spectroscopic properties of large systems.

Quantum dynamics simulation and computational spectroscopy serve as indispensable tools for the theoretical understanding of various fundamental physical and chemical processes, ranging from charge transfer to photochemical reactions. When simulating realistic systems, the primary challenge stems from the overwhelming number of degrees of freedom and the pronounced many-body correlations. Here, we present Kylin-V, an innovative quantum dynamics package designed for accurate and efficient simulations of dynamics and spectroscopic properties of vibronic Hamiltonians for molecular systems and their aggregates. Kylin-V supports various quantum dynamics and computational spectroscopy methods, such as time-dependent density matrix renormalization group and our recently proposed single-site and hierarchical mapping approaches, as well as vibrational heat-bath configuration interaction. In this paper, we introduce the methodologies implemented in Kylin-V and illustrate their performances through a diverse collection of numerical examples.

On Generalized Two Dimensional Linear Hybrid Dynamical Systems

On Generalized Two Dimensional Linear Hybrid Dynamical Systems

Dynamical properties of a diffusion-coupled system of differential equations with an additional internal coupling

Dynamical properties of a diffusion-coupled system of differential equations with an additional internal coupling

Investigation of structural, electrical, dynamical, optical, and thermoelectric properties of Sr-doped Mg2Si systems using first-principles calculations

Investigation of structural, electrical, dynamical, optical, and thermoelectric properties of Sr-doped Mg2Si systems using first-principles calculations

Proposal and Evaluation of Vertical Vibration Theory of Air Caster

Urbanization and human development have increased the exposure of seismic risk. Therefore, engineers need to develop new and more efficient technologies to protect people and objects from the disastrous consequences of earthquakes. Air casters have gained attention and have been utilized in the past decade as effective seismic vibration control devices. Although such active isolation systems perform well in mitigating horizontal input vibrations, they might cause excessive rocking motions, if not designed properly. This fact emphasizes the importance of exploring the vertical dynamic properties of air isolation systems. To gain such an understanding, this research examines and proposes a formula for the vertical stiffness and damping of air caster systems. Theoretical solutions to the vertical stiffness and damping of such systems have been explored. Computer simulations considering fluid-structure interaction have also been performed to understand the dynamic behavior of the supporting air layer. Results have been compared to validate the proposed dynamic quantities within the considered simulation range. It is also concluded that the instantaneous air layer thickness, representing the air chamber pressure, and the bearing inlet flow rate are the key factors in determining the dynamic properties of the air layer. It is concluded that to evaluate the performance of the air caster seismic isolation device and increase the probability that the qualified seismic isolation performance will be exhibited, it is necessary to investigate which parameters are greatly involved in the viscous damping coefficient and the spring constant of amass-spring-damper system equivalent to the air caster isolation system.

Complex dynamical behaviors of a honeybee-mite model in parameter plane

The honeybee has a significant impact on ecosystem stability, biodiversity conservation, and pollinating crops. However, during the past few years, there has been a sharp reduction in both the honeybee population and their colonies. It has been found that the parasitic mite Varroa destructor is responsible for the decline in honeybee colonies around the world, which in turn immensely affects the economic growth of a country. To investigate how the dynamics of a system is influenced by the growth of honeybees and the parasitism of mites, we study a nonlinear honeybee-mite population model in a discrete-time setup. We observe that an increase in the value of the queen’s egg-laying rate drives the system towards chaos. However, chaos can be controlled as well if the parasite attachment effect is increased. The intrinsic dynamical properties of the proposed system are investigated with the simultaneous variation of the queen’s egg-laying rate and the mite’s parasite attachment effect by constructing several largest Lyapunov exponent and isoperiodic diagrams. The investigation reveals the existence of several periodic structures in the quasiperiodic and chaotic regimes of the parameter plane, including Arnold tongues, saddle area, spring area, connected shrimp-shaped structure, and connected saddle area. We also find the appearance of a novel ‘jellyfish’-shaped periodic structure. One of the most fascinating findings of this study is the appearance of Arnold tongues along the inner boundary region of another Arnold tongue. In addition, this work also reveals different types of multistability, e.g., the coexistence of two, three, and even four attractors. What is more interesting is that the current analysis unveils the coexistence of five attractors as well, more specifically, four different periodic attractors coexist with the trivial fixed point attractor, which is quite rare in ecological systems. The structures of the basins of these coexisting attractors are either smooth or very complex in nature. Furthermore, the present study also discloses the fact that variation in the initial condition of the system can significantly change the appearance of the periodic structures in the parameter plane.

Basin stability for updating system uncertainties.

In this paper, we propose an application of the basin stability tool which allows us to update the information on the system properties under parameter uncertainties. The concept is presented using a classical mechanical setup of coupled pendula, exchanging the energy via the supporting structure. Depending on the support parameters, the model can exhibit different types of coexisting synchronous patterns as well as remaining desynchronized. We calculate basin stability maps of particular behaviors and combine them with prior parameter distributions using Bayesian inference. The obtained posterior distributions, based on the attractor occurrence, update our knowledge on the system properties in the terms of probabilities. We also underline the problem of evaluating basin stability close to the existence borders, comparing the classical approach of fixed parameters with the one involving variations. The differences between the estimation methods can have a crucial meaning for the discussed application and should be considered carefully. The results presented in this paper uncover ways of applying the basin stability concept, which can be used to study the properties of complex dynamical systems from a probability perspective.

Spectro-photometry of Phobos simulants: I. Detectability of hydrated minerals and organic bands

Previous Mars Reconnaissance Orbiter and Mars Express observations of Phobos and Deimos, the moons of Mars, have improved our understanding of these small bodies. However, their formation and composition remain poorly constrained. Physical and spectral properties suggest that Phobos may be a weakly thermal-altered captured asteroid but the dynamical properties of the martian system suggest a formation by giant collision similar to the Earth moon. In 2027, the JAXA’s MMX mission aims to address these outstanding questions.We undertook measurements with a new simulant called OPPS (Observatory of Paris Phobos Simulant) which closely matches Phobos reflectance spectra from the visible to the mid-infrared wavelength range. The simulant was synthesized using a mixture of olivine, saponite, anthracite, and coal.Since observation geometry strongly influences the photometry and spectra of the light reflected from planetary surfaces, we evaluated the parameters obtained by modeling the phase curves – obtained through laboratory measurements – of two different Phobos simulants (UTPS-TB and OPPS) using Hapke IMSA model. Our results show that the photometric properties of Phobos simulants are not fully consistent with those of carbonaceous chondrites and martian meteorites. We also investigated the detection of volatiles/organic compounds and hydrated minerals, as the presence of such components is expected on Phobos in the hypothesis of a captured primitive asteroid. To investigate their detectability, we examined the variability of the 3.28μm and 3.42μm absorption bands related to aliphatic/aromatic carbon (as a proxy of organic material), as well as the 2.7μm O–H feature in a Phobos laboratory spectroscopic simulant. The results indicate that a significant amount of organic compounds is required for the detection of C–H bands at 3.4μm. The bands at 3.28 and 3.42μm are faint (less than 2%) when ∼3 wt% of organic compounds are present in the simulant and are likely undetectable by the MIRS spectrometer onboard the MMX mission. When the concentration of aliphatic and aromatic compounds is increased to 6 wt%, a positive detection starts to become more plausible using remote sensing infrared spectroscopy. In contrast, the 2.7μm absorption band, due to hydrated minerals, is much deeper and easier to detect than C–H organic features at the same concentration levels. The feature is still clearly detectable even when the simulant contains only 3 vol.% of phyllosilicates, corresponding to 0.7 wt% OH groups.Posing limits on detectability of some possible key components of Phobos surface will be pivotal to prepare and interpret future observations of the MIRS spectrometer as well as TENGOO and OROCHI cameras onboard MMX mission.

Level statistics of the one-dimensional dimerized Hubbard model

The statistical properties of level spacings provide valuable insights into the dynamical properties of a many-body quantum systems. We investigate the level statistics of the Fermi–Hubbard model with dimerized hopping amplitude and find that after taking into account translation, reflection, spin and η pairing symmetries to isolate irreducible blocks of the Hamiltonian, the level spacings in the limit of large system sizes follow the distribution expected for hermitian random matrices from the Gaussian orthogonal ensemble. We show this by analyzing the distribution of the ratios of consecutive level spacings in this system, its cumulative distribution and quantify the deviations of the distributions using their mean, standard deviation and skewness.

Existence and stability of a quasi-periodic two-dimensional motion of a self-propelled particle

The mechanism of self-propelled particle motion has attracted much interest in mathematical and physical understanding of the locomotion of living organisms. In a top-down approach, simple time-evolution equations are suitable for qualitatively analyzing the transition between the different types of solutions and the influence of the intrinsic symmetry of systems despite failing to quantitatively reproduce the phenomena. We aim to rigorously show the existence of the rotational, oscillatory, and quasi-periodic solutions and determine their stabilities regarding a canonical equation proposed by Koyano et al. (J Chem Phys 143(1):014117, 2015) for a self-propelled particle confined by a parabolic potential. In the proof, the original equation is reduced to a lower dimensional dynamical system by applying Fenichel’s theorem on the persistence of normally hyperbolic invariant manifolds and the averaging method. Furthermore, the averaged system is identified with essentially a one-dimensional equation because the original equation is O(2)-symmetric.

On the dynamics and wear properties of dry friction bearings in motor rotor system considering rough surface contact damping

Maintaining rotor stability and reducing bearing wear hold practical significance for the rotor system. However, the dynamic properties of rotor system supported by dry friction bearings are unknown, hindering effective bearing optimization. To tackle this issue, a 5-degree-of-freedom dynamics model is established for the motor rotor system of the outdoor unit supported by porous bearings. The rough surface damping contact model is employed to calculate the contact performance of the dry friction bearings. The effects of bearing edge modification on system dynamics and bearing wear properties are investigated and compared with well-lubricated bearings. The results demonstrate that an appropriate amount of edge modification can decelerate the impact between the rotor and the bearings and reduce wear under dry friction conditions.

Contractive Shadowing Property of Dynamical Systems

Contractive Shadowing Property of Dynamical Systems

Fixed Attracting Closed Surfaces in Three and Higher Dimensional Dynamical Systems

Fixed Attracting Closed Surfaces in Three and Higher Dimensional Dynamical Systems

Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges

This paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. The results demonstrate that period-doubling and Hopf bifurcations are two typical routes to generate chaos, as evidenced by the calculation of the maximum Lyapunov exponents near the critical bifurcation points. Finally, a feedback control method is suggested, utilizing feedback of system states and perturbation of feedback parameters, to efficiently manage the bifurcations and chaotic attractors of the discrete predator-prey model.

Experimental studies of the impact of fluid sloshing in the tank on the dynamic characteristics of the “wing model – fuel tank” system

Flexible response of the airframe structural elements under operational loads are one of the main sources of fatigue damage accumulation. It is known that fuel sloshing in tanks can change the dynamic (frequencies and shapes of natural oscillations) and dissipative properties (oscillation damping decrements) of an elastic system, including partially or completely fuelfilled tanks. It is specified that fuel sloshing in tanks due to the additional oscillation energy dissipation of the elastic system can have a significant impact on both the fatigue and aeroelastic characteristics of aircraft structural elements. Theoretical and experimental studies, applicably to the majority of currently operating transport aircraft, have shown that when modeling dynamic phenomena and solving aeroelasticity problems, fuel can be considered conditionally solidified, which actually does not affect the resultant effect. The advent of modern heavy transport aircraft with a high aspect ratio wing and four engines on pylons under the wing has led to a considerable change in the dynamic picture of the aircraft interaction with the environment. The main feature is that, under this arrangement, the first horizontal bending mode of the wing is embedded in the main flexible modes that determine the dynamic response to external effects. In this case, the model of solidified fuel can have a significant impact on the accuracy of predicting dynamic loads and, as a consequence, on the quantitative characteristics of durability and aeroelasticity. The article presents the results of experimental studies of the impact of fluid sloshing in the tank on the dynamic characteristics (frequencies of natural oscillations and amplitudes of forced oscillations) of the “wing model – fuel tank” system. The design of the experimental installation and the methodology of conducting experiments are described. During the experiment, the tank was partially filled with liquid or full, and horizontal bending modes of the wing model, for which considering liquid sloshing in the tank is the most relevant, were studied. The tank refueling levels are determined at which the maximum effect of the system oscillation damping is achieved due to energy dissipation under liquid sloshing. The effect of various factors (presence of a top cover, internal structural frame, perforation in the structural frame) on the amplitudes and frequencies of forced oscillations is analyzed.

The role of taxation in an integrated economic-environmental model: a dynamical analysis

AbstractWe propose a model with economic and environmental domains that interact with each other. The economic sphere is described by a Solow growth model, in which productivity is not exogenous but negatively affected by the stock of pollution that stems from the production process. A regulator can charge a tax on production, and the resources collected from taxation are used to reduce pollution. The resulting model consists of a two dimensional discrete dynamical system, and we study the role of taxation from both a static and a dynamical point of view. The focus is on the determination of the conditions under which taxation has a positive effect on the environment and leads to economic growth. Moreover, we show that a suitable environmental policy can allow recovering both local and global stability of the steady states. On the contrary, we show that, if the policy is not adequate, the system can exhibit endogenous oscillating and chaotic behavior and multistability phenomena.