Dynamics

This article proposes a method for forming invariant stochastic differential systems, namely dynamic systems with trajectories belonging to a given smooth manifold. The Itô or Stratonovich stochastic differential equations with the Wiener component describe dynamic systems, and the manifold is implicitly defined by a differentiable function. A convenient implementation of the algorithm for forming invariant stochastic differential systems within symbolic computation environments characterizes the proposed method. It is based on determining a basis associated with a tangent hyperplane to the manifold. This article discusses the problem of basis degeneration and examines variants that allow for the simple construction of a basis that does not degenerate. Examples of invariant stochastic differential systems are given, and numerical simulations are performed for them. Full article

The dynamic behaviour of a column excited at the base, e.g., under an earthquake load, has been extensively studied. However, the column may also experience impact at the tip like a heavy-duty truck braking on a bridge. The caused base shear of the pier is very important. In this work, the dynamic behaviour, particularly the impact load from the tip to the base, was studied on two different composites: double basalt- and double flax fibre-reinforced polymer tube (DBFRP and DFFRP)-confined coconut fibre-reinforced concrete (CFRC). For each composite, two columns with a height of 1 m, an inner diameter of the outer tube of 100 mm, and an inner tube of 30 mm were fabricated. The column was fully fixed at the base and struck at the top with an impulse hammer. The base shear was calculated through an equivalent mass method using the acceleration at the tip. The results show that both DBFRP-CFRC and DFFRP-CFRC can dissipate a portion of the impact force, resulting in a reduction in force at the base of the specimens. The base shear of DFFRP-CFRC columns is larger and dissipates energy faster than that of DBFRP-CFRC columns. Full article

Empirical debates about a “crisis of trust” highlight long-lived pockets of high trust and deep distrust in institutions, as well as abrupt, shock-induced shifts between the two. We propose a probabilistic model in which such phenomena emerge endogenously from social learning on hierarchical networks. Starting from a discrete model on a directed acyclic graph, where each agent makes a binary adoption decision about a single assertion, we derive an effective influence kernel that maps individual priors to stationary adoption probabilities. A continuum limit along hierarchical depth yields a degenerate, non-conservative logistic–diffusion equation for the adoption probability $u(x,t)$, in which diffusion is modulated by $(1-u)$ and increases the integral of u rather than preserving it. To account for micro-level uncertainty, we perturb these dynamics by multiplicative Stratonovich noise with amplitude proportional to $u(1-u)$, strongest in internally polarised layers and vanishing at consensus. At the level of a single depth layer, Stratonovich–Itô conversion and Fokker–Planck analysis show that the noise induces an effective double-well potential with two robust stochastic phases, $u\approx 0$ and $u\approx 1$, corresponding to persistent distrust and trust. Coupled along depth, this local bistability and degenerate diffusion generate extended domains of trust and distrust separated by fronts, as well as rare, Kramers-type transitions between them. We also formulate the associated stochastic partial differential equation in Martin–Siggia–Rose–Janssen–De Dominicis form, providing a field-theoretic basis for future large-deviation and data-informed analyses of trust landscapes in hierarchical societies. Full article

Multi-revolution Lambert solvers are intended to find the elliptic transfer orbits that are traveled multiple times and connect two specified positions in prescribed time, under the assumption of considering natural (Keplerian) orbital motion in the presence of a single attracting body. This study proposes and tests a new, effective multi-revolution Lambert solver that employs the initial true anomaly, which identifies the initial position along the transfer ellipse, as the unknown variable. The related search interval is identified through closed-form expressions for upper and lower bounds. A simple numerical algorithm is developed and employed over the entire search interval to detect all Lambert solutions. The new multi-revolution solver proposed in this work is simple to understand and easy to implement and is successfully tested in several challenging scenarios (corresponding to some pathological cases reported in the recent scientific literature), as well as for the study of Earth–Mars interplanetary transfers. Comparison with alternative, up-to-date techniques points out that the new approach at hand is able to detect all the feasible transfer ellipses, in all cases, with very satisfactory accuracy in terms of final position error, even in challenging scenarios that include a huge number of revolutions or near-antipodal terminal positions. Full article

The uneven distribution of flow in water distribution networks (WDNs) can cause inefficient flows and pressure imbalances as well as degraded water quality in areas where demand is higher than the networks’ design limit. In this study, two faulty connections within a WDN in Greece that exhibited unusual geometric shapes favoring preferential flow paths were investigated. The three-dimensional computational fluid dynamics simulations were performed in ANSYS Fluent solver (v. 23.1) to study the internal behavior of this network for steady-state flows. The standard k-ε model was employed to calculate turbulence and energy losses in this network. In Connection A, which is a cross-shaped junction with two inlets and two outlets, and in Connection B, which is a complex 4 → 1 → 4 manifold connection, more than 80% of total inflow was found to be directed to a single outlet. The pressure contour plots revealed that this is due to the large total head losses associated with pronounced changes in flow direction. The role of explicit junction losses in network modeling and network improvements to improve hydraulic behavior has thereby gained prominence through this study. The applicability and capability of computational fluid dynamics in characterizing complex flow problems in urban WDNs have thereby proven to be significant. Full article

Circuit implementation is a widely accepted method for validating theoretical insights observed in chaotic systems. It also serves as a basis for numerous chaos-based engineering applications, including data encryption, random number generation, secure communication, neuromorphic computing, and so forth. To get feasible, compact, and cost-effective circuit implementations of chaotic systems, the underlying mathematical model may be simplified while preserving all rich nonlinear behaviors. In this framework, this manuscript presents a simplified Hopfield Neural Network (HNN) capable of generating a broad spectrum of complex behaviors using a minimal number of electronic elements. Based on Shil’nikov’s theorem for heteroclinic orbits, the number of non-zero synaptic connections in the matrix weights is reduced, while simultaneously using only one nonlinear activation function. As a result of these simplifications, we obtain the most compact electronic implementation of a tri-neuron HNN with the lowest component count but retaining complex dynamics. Comprehensive theoretical and numerical analyses by equilibrium points, density-colored continuation diagrams, basin of attraction, and Lyapunov exponents, confirm the presence of periodic oscillations, spiking, bursting, and chaos. Such chaotic dynamics range from single-scroll chaotic attractors to double-scroll chaotic attractors, as well as coexisting attractors to transient chaos. A brief security application of an S-Box utilizing the presented HNN is also given. Finally, a physical implementation of the HNN is given to confirm the proposed approach. Experimental observations are in good agreement with numerical results, demonstrating the usefulness of the proposed approach. Full article

The proposed work introduces a sizing algorithm to achieve a desired linear transconductance in the optimization of operational transconductance amplifiers (OTAs) by applying the $g_m/I_D$ method to find the initial width (W) and length (L) sizes of the transistors. These size values are used to run the non-dominated sorting genetic algorithm (NSGA-II) to perform a multi-objective optimization of three OTA topologies. The $g_m/I_D$ method begins with transistor characterization using MATLAB R2024a generated look-up tables (LUTs), which map normalized transconductance of the transistor channel dimensions, and key performance metrics of a complementary metal–oxide–semiconductor (CMOS) technology. The LUTs guide the initial population generation within NSGA-II during the optimization of OTAs to achieve not only a desired transconductance but also accuracy alongside linearity, high DC gain, low power consumption, and stability. The feasible W/L size solutions provided by NSGA-II are used to enhance the CMOS design of a memristor emulator, where the OTA with the desired transconductance is adapted to tune the behavior of the memristor, demonstrating improved pinched hysteresis loop characteristics. In addition, process, voltage and temperature (PVT) variations are performed by using TSMC 180 nm CMOS technology. The memristor-based on optimized OTAs is used to design a Leaky Integrate-and-Fire (LIF) neuron, which produces identical spike counts (seven spikes) under the same input conditions, though the time period varied with a CMOS inverter scaling. It is shown that increasing transistor widths by 100 in the inverter stage, the spike quantity is altered while changing the spiking period. This highlights the role of device sizing in modulating LIF neuron dynamics, and in addition, these findings provide valuable insights for energy-efficient neuromorphic hardware design. Full article

Diffusion on curved surfaces deviates from the flat case due to geometrical corrections in the evolution of its moments, such as the geodesic mean square displacement. Moreover, anomalous diffusion is widely used to model transport in disordered, confined, or crowded environments and can be described by a temporal subordination scheme, leading to a time-fractional diffusion equation. In this work, we analyze the dynamics of time subordinated anomalous diffusion on curved surfaces. By using a generalized Taylor expansion with fractional derivatives in the Caputo sense, we express the moments as a temporal power series and show that the anomalous exponent couples with curvature terms, leading to a competition between geometric and anomalous effects. This coupling indicates a mechanism through which curvature modulates anomalous transport. Full article

This research investigates the seismic behavior of continuous-span base-isolated bridges integrated with fluid inerter damper (FID) through a linear analytical framework under recorded earthquake excitations. The resisting mechanism of the FID is modelled as a combination of inertial and viscous forces, which are functions of the relative acceleration and velocity between connected nodes. Linear time-history simulations and a series of parametric analyses are conducted to examine how variations in inertance, damping ratio, and installation location affect key seismic response parameters, including deck acceleration, bearing displacement, and substructure base shear. Comparative analyses with conventional viscous dampers and isolation alone establish the relative effectiveness of FID. Analysis indicates that FID effectively reduces deck accelerations through apparent mass amplification, suppresses bearing displacements via viscous damping, and redistributes seismic forces depending on placement strategies. An optimum inertance range is identified that minimizes accelerations without amplifying base shear, with abutment-level placement proving most effective for pier shear control, while intermediate placement provides balanced reductions. Overall, FID consistently outperforms viscous dampers and conventional isolation, underscoring their potential as an advanced inerter-based solution for both new bridge design and retrofit applications. Full article

We provide an analytical framework for describing the propagation of light in waveguide arrays, considering both infinite and semi-infinite cases. The interaction up to second neighbors is taken into account, which provides a more realistic setup. We show that these solutions follow a distinctive structural pattern. This pattern reflects a transition from conventional Bessel functions to the lesser-known one-parameter generalized Bessel functions, offering new insights into the propagation dynamics in these systems. Full article

In this study, we explore the emergence of generalized synchronization (GS) in arrays of Hindmarsh–Rose (HR) neurons that are coupled through memristive synapses. We design coupling functions utilizing active memristors to facilitate GS in a bidirectionally coupled two-neuron memristive neural network (MNN). Our analysis employs a nearest neighbor (NN) approach. Our findings indicate that there is a threshold coupling strength for the active memristive synapses required to achieve GS. Additionally, we investigate how memristor parameters affect the temporal characteristics of synchronized neuronal firing patterns. Specifically, we discover that the interburst interval (IBI) is directly proportional to the coupling strength of the memristive synapses, while the interspike interval (ISI) is inversely proportional to this strength. Full article

In this paper, we study the different types of trajectories that correspond to a particular orbital behavior of caldera-type Hamiltonian systems. This particular orbital behavior is dynamical matching. Dynamical matching is an important chemical phenomenon that is encountered in many caldera-type organic chemical reactions. In this paper we will distinguish the different types of trajectories that correspond to this phenomenon using periodic orbit dividing surfaces. Full article

This study investigates the combined resonance phenomenon in magneto-electro-elastic (MEE) cylindrical shells under longitudinal and lateral excitations with thermal factors, addressing the complex interaction between mechanical, electrical, and magnetic fields in smart structures. The research aims to establish a theoretical framework for predicting resonance behaviors in energy harvesting and sensing applications. Using Maxwell’s equations and Hamilton’s principle, the governing equations for combined resonance are derived. The method of varying amplitude (MVA) is employed to acquire the combined resonance response across varying parameters. Furthermore, the Runge–Kutta method is applied to investigate the bifurcation and chaotic motion characteristics under different longitudinal and lateral excitation conditions. Key findings reveal the coupling effects of multi-physical fields on resonance frequencies, demonstrating quantitative agreement with prior studies. The results provide fundamental insights into the dynamic characteristics of MEE materials, offering theoretical support for optimizing their performance in adaptive engineering systems. Full article

We develop a four-dimensional nonlinear model of a reflexive financial system by extending the Xin–Zhang system with a self-reinforcing sentiment channel. The model comprises four interacting variables—interest rate, investment demand, price index, and market confidence—and incorporates reflexivity to capture feedback between economic fundamentals and investor sentiment. A Lyapunov function shows that the system is well-posed and dissipative, ensuring bounded trajectories. We then analyse the dynamics using standard nonlinear-dynamics tools. Reflexive confidence sustains chaotic motion, inhibits convergence to equilibria, and produces irregular, aperiodic bifurcation patterns; sentiment-driven feedback destabilises a dissipative macroeconomic model and sustains volatility, as evidenced by a positive largest Lyapunov exponent and Kolmogorov–Sinai entropy greater than zero. Using U.S. monthly consumer sentiment and the S&P 500, we observe co-movement, a medium-horizon lead of sentiment, and a nonlinear persistence map $w_{t+1}=f\left(w_t\right)$—stylised facts consistent with the model’s self-reinforcing confidence channel. Full article

We propose a Ramsey approach to the dimensional analysis of physical systems, which complements the seminal Buckingham theorem. Dimensionless constants describing a given physical system are represented as vertices of a graph, referred to as a dimensions graph. Two vertices are connected by an aqua-colored edge if they share at least one common dimensional physical quantity and by a brown edge if they do not. In this way, a bi-colored complete Ramsey graph is obtained. The relations introduced between the vertices of the dimensions graph are non-transitive. According to the Ramsey theorem, a monochromatic triangle must necessarily appear in a dimensions graph constructed from six vertices, regardless of the order of the vertices. Mantel–Turán analysis is applied to study these graphs. The proposed Ramsey approach is extended to graphs constructed from fundamental physical constants. A physical interpretation of the Ramsey analysis of dimensions graphs is suggested. A generalization of the proposed Ramsey scheme to multi-colored Ramsey graphs is also discussed, along with an extension to infinite sets of dimensionless constants. The introduced dimensions graphs are invariant under rotations of reference frames, but they are sensitive to Galilean and Lorentz transformations. The coloring of the dimensions graph is independent of the chosen system of units. The number of vertices in a dimensions graph is relativistically invariant and independent of the system of units. Full article

The problem of nonlinear elastic transverse oscillations of a beam moving along its axis and subjected to an axial compressive or tensile force is considered. A theoretical study is carried out using the asymptotic method of nonlinear mechanics KBM (Krylov–Bogolyubov–Mitropolsky). Using this methods, differential equations were obtained in a standard form, determining the law of variation in amplitude and frequency as functions of kinematic, force, and physico-mechanical parameters in both resonant and non-resonant regimes. The fourth-order Runge–Kutta method was applied for the oscillatory system numerical analysis. The computation of complex mathematical expressions and graphical representation of the results were implemented in the mathematical software Maple 15. The results obtained can be applied for engineering calculations of structures containing moving beams subjected to compressive or tensile forces. Full article

We investigate the Cauchy problem for a heat equation incorporating variable diffusion coefficients and fractional memory effects modeled by a separable convolution kernel. By employing the fundamental solution of the associated parabolic equation, the problem is reformulated as a Volterra-type integral equation. Under appropriate regularity assumptions, we establish existence and uniqueness of classical solutions. Furthermore, we address an inverse problem aimed at simultaneously recovering the memory kernel and the solution. Using a differentiability-based approach, we derive a stable and well-posed formulation that enables the identification of memory effects in fractional heat models. Full article

This paper presents two classic analog oscillators: a relaxation oscillator and a Wien bridge one, where a memristor replaces a resistor. The circuits are simulated in TopSPICE 7.12 using a memristor emulation circuit and commercially available components to evaluate the memristor’s impact. In the case of the relaxation oscillator, which includes the memristor, a notable increase in oscillation frequency was observed compared to the classical circuit, with a nearly 10-fold increase from 790 Hz to 7.78 kHz while maintaining a constant amplitude. This confirms the influence of the memristor’s dynamic resistance on the circuit time constant. On the other hand, the Wien-bridge oscillator exhibits variations in specific parameters, such as peak voltage, amplitude, and frequency. In this case, the oscillation frequency decreased from 405 Hz to 146 Hz with the addition of the memristor, a characteristic introduced by the proposed memristive element’s nonlinear interactions. Experimental results confirm the feasibility of incorporating memristors into classical oscillator circuits, enabling frequency changes while maintaining stable oscillations, allowing reconfigurable and adaptable analog designs that leverage the properties of memristive devices. Full article

The dynamics of port-Hamiltonian systems is based on energy balance principles (the first law of thermodynamics) embedded in the structure of the model. However, when dealing with thermodynamic subsystems, the second law (entropy production) should also be explicitly taken into account. Several frameworks were developed as extensions to the thermodynamic domain of port-Hamiltonian systems. In our work, we study three of them, namely irreversible port-Hamiltonian systems, entropy-based generalized Hamiltonian systems, and entropy-production-metric-based port-Hamiltonian systems, which represent alternative approaches of selecting the state variables, the storage function, simplicity of physical interpretation, etc. On the example of a simplified lumped-parameter model of a heat exchanger, we study the frameworks in terms of their implementability for an IDA-PBC-like control and the simplicity of using these frameworks for practitioners already familiar with the port-Hamiltonian systems. The comparative study demonstrated the possibility of using each of these approaches to derive IDA-PBC-like thermodynamically consistent control and provided insight into the applicability of each framework for the modeling and control of multiphysics systems with thermodynamic subsystems. Full article