Search Results (103)

This study investigates the nonlinear aeroelastic behavior and energy harvesting performance of a two-degrees-of-freedom NACA 0012 airfoil under varying reduced velocities and electrical load resistances. The system exhibits a range of dynamic responses, including periodic and chaotic states, governed by strong fluid–structure interactions. Nonlinear oscillations first appear near the critical reduced velocity $U_r^{*}=6$, with large-amplitude limit-cycle oscillations emerging around $U_r^{*}=8$ in the absence of the electrical loading. As the load resistance increases, this transition shifts to higher $U_r^{*}$, reflecting the damping effect of the electrical load. Fourier spectra reveal the presence of odd and even superharmonics in the lift coefficient, indicating nonlinearities induced by fluid–structure coupling, which diminishes at higher resistances. Phase portraits and Poincaré maps capture transitions across dynamical regimes, from periodic to chaotic behavior, particularly at a low resistance. The voltage output correlates with variations in the lift force, reaching its maximum at an intermediate resistance before declining due to a suppressing nonlinearity. Flow visualizations identify various vortex shedding patterns, including single (S), paired (P), triplet (T), multiple-pair (mP) and pair with single (P + S) that weaken at higher resistances and reduced velocities. The results demonstrate that nonlinearity plays a critical role in efficient voltage generation but remains effective only within specific parameter ranges. Full article

This study develops a dynamic IS-LM macroeconomic model that incorporates delayed taxation and a memory-dependent income effect, and calibrates it to quarterly data for Romania (2000–2023). Within this framework, fiscal policy lags are modelled using a “memory” income variable that weights past incomes, an approach grounded in distributed lag theory to capture how historical economic conditions influence current dynamics. The model is analysed both analytically and through numerical simulations. We derive stability conditions and employ bifurcation analysis to explore how the timing of taxation influences macroeconomic equilibrium. The findings reveal that an immediate taxation regime yields a stable adjustment toward a unique equilibrium, consistent with classical IS-LM expectations. In contrast, delayed taxation, where tax revenue depends on past income, can destabilise the system, giving rise to cycles and even chaotic fluctuations for parameter values that would be stable under immediate collection. In particular, delays act as a destabilising force, lowering the threshold of the output-adjustment speed at which oscillations emerge. These results highlight the critical importance of policy timing: prompt fiscal feedback tends to stabilise the economy, whereas lags in fiscal intervention can induce endogenous cycles. The analysis offers policy-relevant insights, suggesting that reducing fiscal response delays or counteracting them with other stabilisation tools is crucial for macroeconomic stability. Full article

Fractional calculus plays a central role in modeling memory-dependent processes and complex dynamics across various fields, including control theory, fluid mechanics, and bioengineering. This study introduces an efficient and stable fractional-order iterative method based on the Caputo derivative for solving nonlinear equations. By employing a Taylor series expansion, a local convergence analysis shows that for $\gamma \in (0,1]$, the method achieves a convergence order of $2\gamma +1$. To address challenges related to memory effects and instability in existing approaches, the proposed scheme incorporates parameter optimization through chaos and bifurcation analysis. Dynamical plane analysis reveals that parameter values within chaotic regimes lead to divergence, while those in stable regions converge uniformly. The method’s performance is evaluated using a set of nonlinear models drawn from biomedical engineering, including enzyme kinetics with inhibition, extended glucose–insulin regulation, drug dose–responses, and lung volume–pressure dynamics. Comparative results demonstrate that the proposed approach outperforms existing methods in terms of iteration count, residual error, CPU time, convergence order, fractal behavior, and memory efficiency. These findings underscore the method’s applicability to complex systems characterized by nonlinearity and memory effects in scientific and engineering contexts. Full article

We investigate the stochastic disruption of synchronization patterns in a system of two non-identical Rulkov neurons coupled via an electrical synapse. By analyzing the system deterministic dynamics, we identify regions of mono-, bi-, and tristability, corresponding to distinct synchronization regimes as a function of coupling strength. Introducing stochastic perturbations to the coupling parameter, we explore how noise influences synchronization patterns, leading to transitions between different regimes. Notably, we find that increasing noise intensity disrupts lag synchronization, resulting in intermittent switching between a synchronous three-cycle regime and asynchronous chaotic states. This intermittency is closely linked to the structure of chaotic transient basins, and we determine a noise intensity range in which such behavior persists, depending on the coupling strength. Using both numerical simulations and an analytical confidence ellipse method, we provide a comprehensive characterization of these noise-induced effects. Our findings contribute to the understanding of stochastic synchronization phenomena in coupled neuronal systems and offer potential implications for neural dynamics in biological and artificial networks. Full article

Fe₃O₄/H₂O nanofluid attracts many researchers’ attention due to its considerable potential for practical applications. This work is focused on the study of heat transfer efficiency in Fe₃O₄/H₂O nanofluids with nanoparticles (NPs) of mean diameter d_NPs in the nanosized range (13–50 nm) at volume fractions up to 2%. The Rayleigh–Bénard problem of free convection between plane-parallel plates corresponding to Rayleigh numbers 10³–10⁷ is numerically solved. It was shown that the addition of up to 2% of NPs with a diameter of 13 nm can increase the Prandtl number by up to 60% compared to pure water. A map of flow regimes is constructed, indicating the emerging convective patterns. It is demonstrated that as the volume fraction of NPs increases, the Prandtl number grows and the transition to more chaotic patterns with Rayleigh number slows down. It is observed that at a Rayleigh number of 10⁴, the heat flux through the nanofluid layer decreases by up to 25% relative to pure water. Conversely, at Ra ≈ 10⁵, the heat flux through the nanofluid layer increases by up to 18% when using a 2% volume fraction of 13 nm diameter NPs. Full article

Modeling complex, non-stationary dynamics remains challenging for deterministic neural networks. We present the Chaos-Integrated Synaptic-Memory Network (CISMN), which embeds controlled chaos across four modules—Chaotic Memory Cells, Chaotic Plasticity Layers, Chaotic Synapse Layers, and a Chaotic Attention Mechanism—supplemented by a logistic-map learning-rate schedule. Rigorous stability analyses (Lyapunov exponents, boundedness proofs) and gradient-preservation guarantees underpin our design. In experiments, CISMN-1 on a synthetic acoustical regression dataset (541 samples, 22 features) achieved R² = 0.791 and RMSE = 0.059, outpacing physics-informed and attention-augmented baselines. CISMN-4 on the PMLB sonar benchmark (208 samples, 60 bands) attained R² = 0.424 and RMSE = 0.380, surpassing LSTM, memristive, and reservoir models. Across seven standard regression tasks with 5-fold cross-validation, CISMN led on diabetes (R² = 0.483 ± 0.073) and excelled in high-dimensional, low-sample regimes. Ablations reveal a scalability–efficiency trade-off: lightweight variants train in <10 s with >95% peak accuracy, while deeper configurations yield marginal gains. CISMN sustains gradient norms (~2300) versus LSTM collapse (<3), and fixed-seed protocols ensure <1.2% MAE variation. Interpretability remains challenging (feature-attribution entropy ≈ 2.58 bits), motivating future hybrid explanation methods. CISMN recasts chaos as a computational asset for robust, generalizable modeling across scientific, financial, and engineering domains. Full article

The peculiar electronic properties of graphene, including the universal dc conductivity and the pseudodiffusive shot noise, are usually found in a small vicinity close to the charge neutrality point, away from which the electron’s effective mass raises, and nanostructures in graphene start to behave similarly to familiar Sharvin contacts in semiconducting heterostructures. Recently, it was pointed out that as long as abrupt potential steps separate the sample area from the leads, some graphene-specific features can be identified relatively far from the charge neutrality point. These features include greater conductance reduction and shot noise enhancement compared to the standard Sharvin values. The purpose of this paper is twofold: First, we extend the previous analysis based on the effective Dirac equation, and derive the formulas that allow the calculation of the arbitrary charge transfer cumulant for doped graphene. Second, the results of the analytic considerations are compared with numerical simulations of quantum transport on the honeycomb lattice for selected nanosystems for which considerations starting from the Dirac equation cannot be directly adapted. For a wedge-shaped constriction with zigzag edges, the transport characteristics can be tuned from graphene-specific (sub-Sharvin) values to standard Sharvin values by varying the electrostatic potential profile in the narrowest section. A similar scenario is followed by the half-Corbino disk. In contrast, a circular quantum dot with two narrow openings showing a mixed behavior appears: the conductance is close to the Sharvin value, while the Fano factor approaches the value characterizing the symmetric chaotic cavity. Carving a hole in the quantum dot to eliminate direct trajectories between the openings reduces the conductance to sub-Sharvin value, but the Fano factor is unaffected. Our results suggest that experimental attempts to verify the predictions for the sub-Sharvin transport regime should focus on systems with relatively wide openings, where the scattering at the sample edges is insignificant next to the scattering at the sample–lead interfaces. Full article

In this paper, we study the synchronization of dissipative quantum harmonic oscillators in the framework of a quantum open system via the active–passive decomposition (APD) configuration. We show that two or more quantum systems may be synchronized when the quantum systems of interest are embedded in dissipative environments and influenced by a common classical system. Such a classical system is typically termed a controller, which (1) can drive quantum systems to cross different regimes (e.g., from periodic to chaotic motions) and (2) constructs the so-called active–passive decomposition configuration, such that all the quantum objects under consideration may be synchronized. The main finding of this paper is that we demonstrate that the complete synchronizations measured using the standard quantum deviation may be achieved for both stable regimes (quantum limit circles) and unstable regimes (quantum chaotic motions). As an example, we numerically show in an optomechanical setup that complete synchronization can be realized in quantum mechanical resonators. Full article

This study examines abrupt changes in system dynamics, focusing on a Hassell-type density-dependent model with an Allee effect. It aims to analyze tipping points leading to extinction and bistability, including chaotic dynamics. Key methods include computing the topological entropy and Lyapunov exponents when varying the carrying capacity, the intrinsic growth rate and the initial conditions, providing a detailed characterization of chaotic regimes. Meanwhile, we derive an inverse square-root scaling law near a saddle-node bifurcation using a complex analysis. This study uniquely integrates chaos theory, a bifurcation analysis and scaling laws into a density-dependent ecological model with an Allee effect, revealing how chaotic regimes, bistability and an analytically derived inverse square-root scaling law near extinction shape the tipping point dynamics and critical transitions in ecological systems. Full article

In this article, we introduce a novel approach to numerical integration based on a modified composite diagonal (CD) method, which is a variation of the semi-implicit Euler–Cromer method. This approach enables the finite-difference scheme to maintain the dynamic regime of the solution while adjusting the integration time step. This makes it possible to implement variable-step integration. We present a variable-step MCD (VS-MCD) version with a simple and stable Hairer step size controller. We show that the VS-MCD method is capable of changing the dynamics of the solution by changing the symmetry coefficient (reflecting the ratio between two internal steps within the composition step), which is useful for tuning the dynamics of the obtained discrete model, with no influence of the appropriate step size. We illustrate the practical application of the developed method by constructing a direct chaotic communication system based on the Sprott Case S chaotic oscillator, demonstrating high values in the largest Lyapunov exponent (LLE). The tolerance parameter of the step size controller is used as the modulation parameter to insert a message into the chaotic time series. Through numerical experiments, we show that the proposed modulation scheme has competitive robustness to noise and return map attacks in comparison with those of modulation methods based on fixed-step solvers. It can also be combined with them to achieve an extended key space. Full article

We consider a circular motion problem related to blind search in confined space. A particle moves in a unit circle in discrete time to find the escape channel and leave the circle through it. We first explain how the exit time depends on the initial position of the particle when the channel width is fixed. We then investigate how narrowing the channel moves the system from discrete changes in the exit time to the ultimate ‘countable chaos’ state that arises in the problem when the channel width becomes infinitely small. It will be shown in the paper that inherent randomness exists in the problem due to the nature of circular motion as the number $\pi$ acts as a random number generator in the system. Randomness of the decimal digits of $\pi$ results in sensitive dependence on initial conditions in the system with an infinitely narrow channel, and we argue that even a simple linear dynamical system can exhibit features of chaotic behaviour, provided that the system has inherent noise. Full article

Growing demands for self-powered, low-maintenance devices—especially in sensor networks, wearables, and the Internet of Things—have intensified interest in capturing ultra-low-frequency ambient vibrations. This paper introduces a hybrid energy harvester that combines elastic buckling with magnetically induced forces, enabling programmable transitions among monostable, bistable, and multistable regimes. By tuning three key parameters—buckling amplitude, magnet spacing, and polarity offset—the system’s potential energy landscape can be selectively shaped, allowing the depth and number of potential wells to be tailored for enhanced vibrational response and broadened operating bandwidths. An energy-based modeling framework implemented via an in-house MATLAB^® R2024B code is presented to characterize how these parameters govern well depths, barrier heights, and snap-through transitions, while an inverse design approach demonstrates the practical feasibility of matching industrially relevant target force–displacement profiles within a constrained design space. Although the present work focuses on systematically mapping the static potential landscape, these insights form a crucial foundation for subsequent dynamic analyses and prototype validation, paving the way for advanced investigations into basins of attraction, chaotic transitions, and time-domain power output. The proposed architecture demonstrates modularity and tunability, holding promise for low-frequency energy harvesting, adaptive vibration isolation, and other nonlinear applications requiring reconfigurable mechanical stability. Full article

This paper introduces a novel chaotic finance system derived by incorporating a modeling uncertainty with an absolute function nonlinearity into existing financial systems. The new system, based on the works of Gao and Ma, and Vaidyanathan et al., demonstrates enhanced chaotic behavior with a maximal Lyapunov exponent (MLE) of 0.1355 and a fractal Lyapunov dimension of 2.3197. These values surpass those of the Gao-Ma system (MLE = 0.0904, Lyapunov dimension = 2.2296) and the Vaidyanathan system (MLE = 0.1266, Lyapunov dimension = 2.2997), signifying greater complexity and unpredictability. Through parameter analysis, the system transitions between periodic and chaotic regimes, as confirmed by bifurcation diagrams and Lyapunov exponent spectra. Furthermore, multistability is demonstrated with coexisting chaotic attractors for p = 0.442 and periodic attractors for p = 0.48. The effects of offset boosting control are explored, with attractor positions adjustable by varying a control parameter k, enabling transitions between bipolar and unipolar chaotic signals. These findings underline the system’s potential for advanced applications in secure communications and engineering, providing a deeper understanding of chaotic finance models. Full article

We have systematically investigated how the strength of optical feedback (OFB) affects the dynamics, noise levels, and photon number probability density distribution (PNPDD) in time-delayed semiconductor lasers (SLs). We find that intensity noise decreases in both weak and strong OFB regimes. The shape of the PNPDDs changes based on OFB strength: it shifts from symmetric to asymmetric based on the OFB strength. In the chaotic region, the PNPDDs display a peak at low intensity and taper off at multiples of the average photon number. The results of this work suggest that operating SLs under weak or strong OFB conditions may help to minimize instability. Full article

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 (EWS) 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. Full article