Dynamics, Volume 5, Issue 3 (September 2025) – 17 articles

Chemical synaptic coupling is crucial in the nervous system. This paper establishes a chemical synaptic Chay neuronal coupling system using the Heaviside function and analyzes the equilibrium point’s type and stability based on the Jacobian matrix. Matcont simulation found that the Hopf bifurcation point transformed into a Bogdanov–Takens bifurcation point under the influence of chemical coupling strength, and a series of saddle-node bifurcation points are generated. The discharge time history of the system and the evolution of single-parameter bifurcation behavior were numerically simulated through a language and Matlab. The parameter matching results indicated that the chemical synaptic reversible potentials and synaptic thresholds were −15 mV and −35 mV, respectively. The bifurcation behavior and its changes under multi-parameter conditions were studied by using various numerical methods such as time series diagrams, bifurcation diagrams, and two-parameter diagrams. The similarity function identified key factors affecting synchrony in a chemical synaptic coupling system. Results indicate that synchrony primarily depends on chemical coupling strength, with other factors providing positive feedback to enhance it. The simulation of the spatiotemporal dynamics in a chemically synaptic coupled network of 2000 ring neurons revealed that altering the maximum conductance at local positions within the network can induce the generation of traveling waves. Strong coupling strengths ensure that the induced traveling waves propagate at greater velocities and can excite and awaken a larger number of neurons in a shorter time frame. The nonlinear properties of chemical synaptic neuronal system offer essential tools and foundations for studying neurobiology and brain dynamics. Full article

The Fluctuation Theorem establishes a relationship between microscopic reversibility and macroscopic irreversible phenomena, such as dissipation. In this short paper, we present an elementary derivation of this theorem within the framework of stochastic thermodynamics. Beginning with a brief examination of the time-reversible laws of motion that rule at the microscopic level, we discuss how through coarse-graining we arrive at the principle of detailed balance. This principle, which was originally proved for equilibrium processes, is extended to out-of-equilibrium situations in order to arrive at the Fluctuation Theorem. Though this extension is theoretically sound, one of the main purposes of this paper is to show that the origin of the practical limitations encountered, when applying this theorem to processes lasting longer than a certain duration, can be explained by the paucity of unlikely events that arise in out-of-equilibrium processes. The numerical results from the one-dimensional, one-particle stochastic model that is introduced here agree very well with the Fluctuation Theorem and, at the same time, bring to light the limits of its applicability in relation to the number of simulations or experiments and the duration of the process under study. Full article

Gear transmission error (GTE) is a critical factor influencing the performance and service life of gear systems, as it directly contributes to vibration, noise generation, and premature wear. The present study introduces a combined theoretical and experimental approach to characterizing GTE in a single-stage spur gear system. A six-degree-of-freedom nonlinear dynamic model was formulated to capture coupled lateral–torsional vibrations, accounting for gear mesh stiffness, bearing and coupling characteristics, and a harmonic transmission error component representing manufacturing and assembly imperfections. Simulations and experiments were conducted under healthy and eccentricity-faulted conditions, where a controlled 890 g eccentric mass induced misalignment. Frequency domain inspection of faulty gear data showed pronounced sidebands flanking the gear mesh frequency near 200 Hz, as well as harmonics extending from 500 Hz up to 1200 Hz, in contrast with the healthy case dominated by peaks confined to 50–100 Hz. STFT analysis revealed dispersed spectral energy and localized high-intensity regions, reinforcing its role as an effective fault diagnostic tool. Experimental findings aligned with theoretical predictions, demonstrating that the integrated modelling and time–frequency framework is effective for early fault detection and performance evaluation of spur gear systems. Full article

The energy potential of sea waves has gained relevance, leading to extensive research on converters. The present work analyzes the contribution of Constructal Design to the development of wave energy converters. Constructal Design utilizes performance indicators to enhance system efficiency by varying the degrees of freedom where flow occurs. Thus, the systematic literature review methodology was applied to gather a collection of documents focused on the research topic. This study identified articles published between 2014 and 2024 by 40 authors affiliated with institutions in Brazil, Italy, and Portugal. The oscillating water column (OWC) converter received the most research attention, followed by the overtopping converter. Analyzing the documents collected for this study, the performance indicators revealed improvements ranging from 1.19 to 839 times, indicating the lowest and highest enhancements observed, respectively. The Constructal Design method has proven highly effective in identifying specific architectures or geometric arrangements that enhance flow configuration and improve the performance of wave energy converters. However, relatively few studies have applied the Constructal Design method to wave energy converters in comparison to other methodologies, presenting a significant opportunity for future research. Full article

Currently, D-fructose (DF) is produced through enzymatic isomerization of beta-D-glucose (DG) under disadvantageous conditions (equilibrium conversion of 50%, costly separation, etc.). Alternatively, the two-step Cetus enzymatic process became a promising approach for producing high-purity DF. First, DG is oxidized to keto-glucose (kDG) using commercial pyranose 2-oxidase (P2Ox). To avoid the fast P2Ox inactivation by the in situ produced hydrogen peroxide, catalase is added to decompose this byproduct. The DG oxidation occurs with high conversion and selectivity, leading to kDG free of allergenic aldose compounds. Then, kDG is reduced to DF by using the NADPH cofactor and aldose reductase (ALR). This study aims to evaluate the continuous in situ regeneration of NADPH at the expense of formate decomposition in the presence of formate dehydrogenase (FDH). By adopting a kinetic model from literature, this in silico analysis determines the optimal operation of a batch reactor (BR) used in the Cetus second step to maximize the DF production and minimize the consumption of costly NADPH. Compared to its simple operation, the optimized BR with cofactor regeneration reported a 25% lower NADPH consumption, though the amount of the processed substrate is ca. 3× higher. Also, the costly enzymes (ALR, FDH) consumption is 2× smaller. Full article

Miller’s rule originated as an empirical relation between the nonlinear and linear optical coefficients of materials. It is now accepted as a useful tool for guiding experiments and computational materials discovery, but its theoretical foundation had long been limited to a derivation for the classical Lorentz model with a weak anharmonic perturbation. Recently, we developed a mathematical framework which enabled us to prove that Miller’s rule is equally valid for quantum anharmonic oscillators, despite different dynamics due to zero-point fluctuations and further quantum-mechanical effects. However, our previous derivation applied only to one-dimensional oscillators and to the special case of second- and third-harmonic generation in a monochromatic electric field. Here we extend the proof to three-dimensional quantum anharmonic oscillators and also treat all orders of the nonlinear response to an arbitrary multi-frequency field. This makes the results applicable to a much larger range of physical systems and nonlinear optical processes. The obtained generalized Miller formulae rigorously express all tensor elements of the frequency-dependent nonlinear susceptibilities in terms of the linear susceptibility and thus allow a computationally inexpensive quantitative prediction of arbitrary parametric frequency-mixing processes from a small initial dataset. Full article

This study aims to develop a new model for windage losses, building upon existing formulation, complemented by dedicated experimental campaigns and a specific methodology designed to isolate and quantify windage losses. The model relies on an analytical approach to flow characterization, incorporating a correction factor accounting for air density reduction. The experimental investigation was carried out on a dedicated test bench and includes both spur and helical gears. The results demonstrate good agreement between the proposed model and the experimental data, with and without the presence of nearby obstacles, such as side flanges, highlighting the model’s robustness across different configurations. The proposed windage loss model reproduces the experimental results with significantly greater accuracy than the original one, yielding relative deviations below 5% compared to almost 20% for spur gears, and below 9% compared to over 21%, and in some cases up to 50%, for helical gears. Full article

The high-dimensional chaos generated in a neural network consisting of pseudo-neuron devices invented by one of the authors (S.N.) has been successfully applied to control the complex motion of a roving robot, e.g., to solve a maze, as reported in the previous papers. On the basis of successful works and the concept that chaos plays important functional roles in biological systems, in the present paper, we report new experiments to show the functional aspects of chaos via behavioral interactions in an ill-posed context and solve problems with chaotic neural networks. Explicitly, experiments on two roving robots in a maze (labyrinth) are reported, in which both seek to catch each other or one chases and the other flees, mimicking the survival activities of insects in natural environments. The two-dimensional robot motion is controlled with motion control systems, each of which is equipped with a chaotic neural network to generate autonomous and adaptive actions depending on sensor inputs of obstacles and/or target detection information including uncertainty. We report both computer experiments and practical hardware implementations, where for the latter, only the chaotic neural network is run on a desktop computer, the motion signals are coded into two-dimensional space, and sensor signals are transferred via Bluetooth device between robots and computers. Full article

We derive a new exactly solvable multi-component system of non-linear evolution equations (NLEEs). The system consists of three $1+1$-dimensional evolution equations—one first-order and two second-order in the spatial variable. We review their Lax representation, formulate the scattering problem, and derive the soliton-like solutions of the system. Full article

This work systematically addresses the dual challenges of non-inertial dynamic coupling and kinematic constraint redundancy encountered in dynamic modeling of serial–parallel–serial hybrid robotic mechanisms, and proposes an improved Newton–Euler modeling method with constraint compensation. Taking the Skiing Simulation Platform with 6-DOF as the research mechanism, the inverse kinematic model of the closed-chain mechanism is established through $G_F$ set theory, with explicit analytical expressions derived for the motion parameters of limb mass centers. Introducing a principal inertial coordinate system into the dynamics equations, a recursive algorithm incorporating force/moment coupling terms is developed. Numerical simulations reveal a 9.25% periodic deviation in joint moments using conventional methods. Through analysis of the mechanism’s intrinsic properties, it is identified that the lack of angular momentum conservation constraints on the end-effector in non-inertial frames leads to system controllability degradation. Accordingly, a constraint compensation strategy is proposed: establishing linearly independent differential algebraic equations supplemented with momentum/angular momentum balance equations for the end platform. Co-Simulation results demonstrate that the optimized model reduces the maximum relative error of actuator joint moments to 0.98%, and maintains numerical stability across the entire configuration space. The constraint compensation framework provides a universal solution for dynamics modeling of complex closed-chain mechanisms, validated through applications in flight simulators and automotive driving simulators. Full article

Schmidt entropy is used as a common denotation for all Hilbert space entropies that can be defined via the Schmidt decomposition theorem; they include quantum entanglement entropies and classical separability entropies. Exact results about the asymptotic growth in time of such entropies (in the form of Renyi entropies of any order $\ge 1$) are directly derived from the Schmidt decompositions. Such results include a proof that pure point spectra entail boundedness in time of all entropies of order larger than 1; and that slower than exponential transport forbids faster than logarithmic asymptotic growth. Applications to coupled Quantum Kicked Rotors and to Floquet systems are presented. Full article

Mid-altitude sounding rockets are essential for atmospheric research and suborbital experimentation, where aerodynamic optimization and structural integrity are crucial for achieving targeted apogees. This study uses OpenRocket v23.09 for preliminary flight performance prediction and SolidWorks 2024 to integrate aerodynamic and structural analyses through Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA). SolidWorks Flow Simulation and SolidWorks Simulation are used to assess how nose cone and fin geometries, as well as thermal deformation, influence flight performance. Among nine tested configurations, the ogive nose cone with trapezoidal fins achieved the highest simulated apogee of 2639 m, with drag coefficients of 0.480 (OpenRocket) and 0.401 (SolidWorks Flow Simulation). Thermal–structural analysis revealed a maximum nose tip displacement of 0.7249 mm for the rocket with the ogive nose cone, leading to an increasing drag coefficient of 0.404. However, thermal deformation of the ellipsoid nose cone led to a reduction in the drag coefficient from 0.419 to 0.399, even though it exhibited a slightly higher maximum displacement of 0.7443 mm. Mesh independence was confirmed with outlet velocity deviations below 1% across refinements. These results highlight the importance of integrated CFD–FEA approaches, geometric optimization, and material resilience for enhancing the aerodynamic performance of subsonic sounding rockets. Full article

We advance a mathematical framework for collective conviction by deriving a continuum theory from the network-based model introduced by us recently. The resulting equation governs the evolution of belief through a degenerate anisotropic logistic–diffusion process, where diffusion slows as conviction saturates. In one spatial dimension, we prove global well-posedness, demonstrate spectral front pinning that arrests the spread of influence at finite depth, and construct explicit traveling-wave solutions. In two dimensions, we uncover a geometric mechanism of curvature–induced quenching, where belief propagation halts along regions of low effective mobility and curvature. Building on this insight, we formulate a variational principle for optimal control under resource constraints. The derived feedback law prescribes how to spatially allocate repression effort to maximize inhibition of front motion, concentrating resources along high-curvature, low-mobility arcs. Numerical simulations validate the theory, illustrating how localized suppression dramatically reduces transverse spread without affecting fast axes. These results bridge analytical modeling with societal phenomena such as protest diffusion, misinformation spread, and institutional resistance, offering a principled foundation for selective intervention policies in structured populations. Full article

The recently proposed conformable deformation of quantum mechanics by a fractional parameter $\alpha \in (0,1]$ has been used to construct a conformable quantum harmonic oscillator, which coincides with the standard quantum oscillator at $\alpha =1$. We argue that there is a conformable generalization of the uncertainty principle and use it to define the conformable coherent states of the conformable quantum oscillator along the general line of quantum mechanics. We investigate the fundamental physical and mathematical properties of these states in the $x^{\alpha }$-representation. In particular, we determine these states from the minimum uncertainty, compute their energy, find their conformable time-dependent form, determine the conformable translation operator, and show that conformable coherent states are eigenstates of the conformable annihilation operator. These states reproduce in the $\alpha =1$ limit of the correspondence principle the coherent states of the standard quantum harmonic oscillator. Full article

We present an analytical framework for describing light propagation in infinite waveguide arrays, incorporating a generalized long-range coupling to achieve a more realistic model. We demonstrate that the resulting solution can be expressed in terms of generalized Bessel-like functions. Additionally, by applying the concept of eigenstates, we borrow from quantum mechanics a basis given in terms of phase states that allows the analysis of the transition from the discrete to the continuum limit, obtaining a relationship between the field amplitudes and the Fourier series coefficients of a given function. We apply our findings to different coupling functions, providing new insights into the propagation dynamics of these systems. Full article

Fractional modeling has emerged as an important resource for describing complex phenomena and systems exhibiting non-local behavior or memory effects, finding increasing application in several areas in physics and engineering. This study presents the analytical derivation of equations pertinent to the modeling of different systems, with a focus on heat conduction. Two specific boundary value problems are addressed: a Helmholtz equation modified with a fractional derivative term, and a fractional formulation of the Laplace equation applied to steady-state heat conduction in circular geometry. The methodology combines the separation of variables technique with fractional power series expansions, primarily utilizing the Caputo fractional derivative. An important aspect of this paper is its instructional emphasis, wherein the mathematical derivations are presented with detail and clarity. This didactic approach is intended to make the analytical methodology transparent and more understandable, thereby facilitating greater comprehension of the application of these established methods to non-integer-order systems. The final goal is not only to provide a different approach of solving these physical models analytically, but to provide a clear, guided pathway for those engaging in the treatment of fractional differential equations. Full article

This research explores how RC columns respond to blast-induced dynamic effects, with a novel focus on partially submerged scenarios, bridging a gap between air blast and underwater explosion (UNDEX) research. Using advanced finite element modeling in LS-DYNA, the study captures the unique behavior of RC columns under mixed-media conditions, where shockwaves propagate through water and air interfaces. Comprehensive parametric analyses explore the influence of charge size, blast stand-off, and depth of water, revealing distinct dampening mechanisms and structural responses. Key findings include a measurable reduction in peak displacement of partially submerged explosions compared to fully submerged explosions, attributed to the moderating effects of the water–air interface. A total of 60 simulation cases were conducted to systematically analyze partially submerged scenarios, providing robust insights into energy transmission and damage mechanisms. The numerical models, validated against published experimental data by others, demonstrate the accuracy of computational modeling in simulating damage profiles, displacement histories, and energy dissipation trends. This research offers practical implications for designing resilient RC structures in coastal and maritime environments. The results contribute significantly to the field of blast mechanics, advancing our understanding of mixed-media shockwave dynamics and their impact on critical infrastructure. Full article