Periodic Regimes Research Articles (Page 1)

This research shows an analytical and numerical analysis of a nonlinear three-dimensional dynamical system controlled by a unique control parameter, named α. The system exhibits self-excited oscillations through local bifurcations for negative α, including saddle-node and supercritical Hopf bifurcations, leading to periodic orbits and a sequence of period-doubling transitions into chaos. On the other hand, when α is negative and there are no equilibrium points, the system shows long term oscillations that last for a long time through hidden attractors—bounded chaotic dynamics with basins of attraction that are not connected to any equilibrium. Numerical continuation and Lyapunov spectrum analysis confirm the simultaneous existence of periodic, quasiperiodic, and chaotic regimes. The results demonstrate the intricate interplay between local bifurcations and global nonlinear frameworks, emphasizing the distinctive routes to chaos and the emergence of hidden dynamics in systems lacking stability.

An important goal in cardiology and other fields is to identify and control dynamic spiral wave patterns in reaction–diffusion partial differential equations. This research focuses on the Barkley model. The spiral wave motion is controlled and suppressed within the Euclidean group rather than through Euclidean symmetry by applying a controller equation. The eigenfunctions associated with the left eigenspace of the adjoint linear equation can be used to characterize the drift or movement of the spiral wave tip trajectory when the system is perturbed. These eigenfunctions provide details regarding how the spiral wave reacts to disruptions. Perturbations to the Barkley system are examined by applying control functions and calculating the principle eigenvalue numerically. The left eigenfunctions of the Barkley equation are determined by solving the left problem associated with the 2D Barkley equation and a 1D dynamical controller. In addition, the control function can be used to suppress the periodic and meandering regimes of the system. In this work, the focus is on the periodic regime.

Although the Belousov–Zhabotinsky (BZ) chemicalreactionhas been the object of intense research efforts for almost a century,many aspects of the BZ complex oscillatory behavior still remain tobe clarified, also due to difficulties in experimentally monitoringthe speciation of the main brominated compounds during the reactioncycles. Herein, we describe an integrated approach based on Br K-edgeX-ray absorption and ultraviolet–visible (UV–vis) spectroscopiesto identify the onset and evolution of concentration-dependent collectivebromine oscillations in the classical BZ reaction. Principal componentanalysis, multivariate curve resolution, and theoretical X-ray spectroscopysimulations were combined to identify the number, nature, and concentrationtime evolution of the key reaction brominated species during the chaoticand periodic BZ regimes. Our integrated approach enabled real-timemonitoring of how variations in metal catalyst concentration influenceboth the metal center and key brominated BZ species throughout thedifferent stages of the complex reaction pathway. The multidisciplinaryexperimental and theoretical approach, sensitive to both the brominatedand metal portions of the BZ system, overcomes the challenges in detectingthe spectroscopically silent BZ reaction species and may be appliedto rationalize a wide range of BZ and non-BZ oscillatory reactions.

This paper presents a detailed study of the (3+1)-dimensional Zakharov–Kuznetsov–Burgers equation to investigate shock-wave phenomena in dusty plasmas with quantum effects. The model provides significant physical insight into nonlinear dispersive and dissipative structures arising in charged-dust–ion environments, corresponding to both laboratory and astrophysical plasmas. We then perform a qualitative, numerically assisted dynamical analysis using bifurcation diagrams, multistability checks, return maps, Poincaré sections, and phase portraits. For both the unperturbed and a perturbed system, we identify chaotic, quasi-periodic, and periodic regimes from these numerical diagnostics; accordingly, our dynamical conclusions are qualitative. We also examine frequency-response and time-delay sensitivity, providing a qualitative classification of nonlinear behavior across a broad parameter range. After establishing the global dynamical picture, traveling-wave solutions are obtained using the Paul–Painlevé approach. These solutions represent shock and solitary structures in the plasma system, thereby bridging the analytical and dynamical perspectives. The significance of this study lies in combining a detailed dynamical framework with exact traveling-wave solutions, allowing a deeper understanding of nonlinear shock dynamics in quantum dusty plasmas. These results not only advance theoretical plasma modeling but also hold potential applications in plasma-based devices, wave propagation in optical fibers, and astrophysical plasma environments.

We present a nanofluidic device enabling single-molecule confinement through free-energy landscapes created by dynamic electrical gating of embedded nanoelectrodes. Unlike static geometric confinement, this system uses a parallel electrode configuration with nanoelectrodes placed in a dielectric layer. Localized electrokinetic fields at electrode wells form tunable attractive potential wells for bimolecular capture. By modulating the voltage bias waveform, the device allows precise control over confinement dynamics, enabling molecular capture, release, and exposure to periodic or stochastic confinement regimes. This flexibility facilitates the study of biomolecular behavior under dynamically adjustable conditions, including controlled confinement fluctuations. The device can manipulate diverse analytes such as double-stranded DNA, liposomes, and DNA nanotubes and facilitates introducing molecules into confined environments intact from bulk while providing enhanced tunability. With the ability to implement tailored confinement profiles, this platform represents a versatile tool for probing molecular confinement and behavior in complex, dynamically varying environments.

Abstract This study presents a novel approximation approach for the Fractional Rössler System using the Variational Iteration Method (VIM). The Fractional Rössler System, an extension of the classical Rössler System, incorporates fractional-order derivatives to capture more intricate dynamical behaviors. VIM is employed due to its efficiency in handling nonlinear fractional differential equations (FDEs) and its novel application to this system. A comparative analysis with the Adams-Bashforth-Moulton method has been conducted, and numerical values are presented to validate the effectiveness of VIM. The graphical results reveal significant chaotic dynamics, including the presence of strange attractors and sensitivity to initial conditions and bifurcation phenomena, indicating transitions between periodic and chaotic regimes. This work provides a new perspective on approximating fractional chaotic systems, demonstrating the potential of VIM in advancing the study of complex dynamical systems.

This study investigates the hydrodynamic behavior of oblate ellipsoidal particles immersed in a uniform flow, focusing on their flow resistance coefficients, including drag, lift, and pitching torque. Using advanced particle-resolved direct numerical simulations (PR-DNS), the research explores fluid-particle interactions across a range of aspect ratios (AR = 1.25, 2.5, 5, 10), orientation angles (0°≤α≤90°), and Reynolds numbers (Rep ≤ 200), relevant to industrial and environmental processes. The simulations reveal significant unsteady flow characteristics past oblate particles with AR larger than 5, and values of Rep larger than 100, resulting in oscillatory behaviors in the hydrodynamic force coefficients, which vary with the aspect ratio of the particle. The contributions of pressure and friction to the force coefficients are analyzed individually, providing insights into how aspect ratio and Reynolds number influence flow behavior. At high Reynolds number, the fluctuations are not negligible and the root mean square (rms) values of flow coefficient fluctuations are also provided, distinguishing between periodic and aperiodic regimes. The results of the accurate unsteady PR-DNS are used to derive novel correlations to predict the drag, lift, and torque coefficients of oblate ellipsoidal particles subject to locally uniform flows. A good agreement is observed between the PR-DNS results and the correlations, with median errors of 1.40%, 2.57%, and 3.09%, for the correlations predicting the drag, lift, and torque coefficients, respectively. These correlations can be used to improve Eulerian–Lagrangian frameworks and provide valuable insights into the role of particle shape and orientation in hydrodynamic interactions within complex flow environments.

In this study, the migratory agricultural pest Spodoptera frugiperda was exposed to three periodic short-term heat stress regimes at 37 °C, 40 °C, and 43 °C (2 h daily), with a constant 26 °C control. We systematically evaluated the effects of periodic thermal stress on developmental traits across all life stages. Combined with 16S rRNA high-throughput sequencing, we analyzed the structural and functional characteristics of the gut bacterial community in adults under heat stress. The results demonstrated that 37 °C exposure accelerated egg-to-adult development, whereas 43 °C markedly extended it. Additionally, 43 °C heat stress suppressed pupation and eclosion rates. Increasing stress temperatures were negatively correlated with pupal weight and body size in both sexes. Notably, 43 °C heat stress caused complete loss of hatching ability in offspring eggs, thereby rendering population reproduction unattainable. 16S rRNA sequencing revealed that Proteobacteria (>90%) dominated the gut bacterial community at the phylum level across all treatments. Under 43 °C heat stress, although female and male adults exhibited an increase in specific bacterial species within their gut bacteria, Alpha diversity analysis revealed no significant differences in the diversity (Shannon index) and richness (Chao index) of gut bacterial communities between sexes under temperature treatments. PICRUSt2 functional prediction indicated that metabolic pathways, biosynthesis of secondary metabolites, and microbial metabolism in diverse environments constituted the dominant functions of gut bacteria in both sexes, while heat stress exerted minimal effects on the functional profiles of gut bacteria in S. frugiperda. These findings not only provide a theoretical basis for predicting summer population dynamics and formulating ecological control strategies for S. frugiperda but also offer critical insights into the adaptive interactions between this pest and its gut bacterial community under heat stress. The results lay a foundation for further exploring the interactions between insect environmental adaptability and bacterial symbiosis.

Semiconductor electronic devices are prone to charge accumulation during production and transportation, which usually causes device breakdown. Ionizers are widely used for electrostatic elimination, and utilizing semiconductor silicon for the discharge needle material in ionizers can effectively prevent metal contamination. To investigate the discharge characteristics of silicon needles and their mode modulation mechanism, this study has established an experimental platform for silicon needle-plate discharge under positive polarity voltage. Discharge pulse parameters and optical signals were measured at varying electrode spacings. The experimental results reveal that silicon needle discharge progresses through four regimes: the spontaneous streamer, the periodic streamer, the cluster streamer, and the glow discharge. Among these, the pulse amplitude is most uniform and stable in the periodic streamer regime. In addition, shorter-gap discharge exhibits higher pulse amplitude and repetition frequency but is easier to transition into the filament regime. The formation process of a single pulse is closely related to the field strength in the ionization region near the needle tip. Hence, parameters such as the pulse rising edge time and falling edge time show minimal variation with voltage. The amount of charge generated per unit time is primarily influenced by the repetition frequency. Consequently, the electrostatic ionizer produces the highest, most stable, and most uniform charges if it operates in the periodic streamer regime.

We investigate the dynamics and the stability of the incompressible flow past a corrugated dragonfly-inspired airfoil in the two-dimensional (2-D) $\alpha {-}Re$ parameter space, where $\alpha$ is the angle of attack and $Re$ is the Reynolds number. The angle of attack is varied in the range of $-5^{\circ } \leqslant \alpha \leqslant 10^{\circ }$ , and $Re$ (based on the free stream velocity and the airfoil chord) is increased up to $Re=6000$ . The study relies on linear stability analyses and three-dimensional (3-D) nonlinear direct numerical simulations. For all $\alpha$ , the primary instability consists of a Hopf bifurcation towards a periodic regime. The linear stability analysis reveals that two distinct modes drive the flow bifurcation for positive and negative $\alpha$ , being characterised by a different frequency and a distinct triggering mechanism. The critical $Re$ decreases as $|\alpha |$ increases, and scales as a power law for large positive/negative $\alpha$ . At intermediate $Re$ , different limit cycles arise depending on $\alpha$ , each one characterised by a distinctive vortex interaction, leading thus to secondary instabilities of different nature. For intermediate positive/negative $\alpha$ , vortices are shed from both the top/bottom leading- and trailing-edge shear layers, and the two phenomena are frequency locked. By means of Floquet stability analysis, we show that the secondary instability consists of a 2-D subharmonic bifurcation for large negative $\alpha$ , of a 2-D Neimark–Sacker bifurcation for small negative $\alpha$ , of a 3-D pitchfork bifurcation for small positive $\alpha$ and of a 3-D subharmonic bifurcation for large positive $\alpha$ . The aerodynamic performance of the dragonfly-inspired airfoil is discussed in relation to the different flow regimes emerging in the $\alpha {-}Re$ space of parameters.

The laminar flow past rectangular prisms is studied in the space of length-to-height ratio ( $1 \leqslant L/H \leqslant 5$ ), width-to-height ratio ( $1.2 \leqslant W/H \leqslant 5$ ) and Reynolds number ( $Re \lessapprox 700$ ); $L$ and $W$ are the streamwise and cross-flow dimensions of the prisms. The primary bifurcation is investigated with linear stability analysis. For large $W/L$ , an oscillating mode breaks the top/bottom planar symmetry. For smaller $W/L$ , the flow becomes unstable to stationary perturbations and the wake experiences a static deflection, vertical for intermediate $W/L$ and horizontal for small $W/L$ . Weakly nonlinear analysis and nonlinear direct numerical simulations are used for $L/H = 5$ and larger $Re$ . For $W/H = 1.2$ and 2.25, the flow recovers the top/bottom planar symmetry but loses the left/right one, via supercritical and subcritical pitchfork bifurcations, respectively. For even larger $Re$ , the flow becomes unsteady and oscillates around either the deflected (small $W/H$ ) or the non-deflected (intermediate $W/H$ ) wake. For intermediate $W/H$ and $Re$ , a fully symmetric periodic regime is detected, with hairpin vortices shed from the top and bottom leading-edge (LE) shear layers; its triggering mechanism is discussed. At large $Re$ and for all $W/H$ , the flow approaches a chaotic state characterised by the superposition of different modes: shedding of hairpin vortices from the LE shear layers, and wake oscillations in the horizontal and vertical directions. In some portions of the parameter space the different modes synchronise, giving rise to periodic regimes also at relatively large $Re$ .

Nonlinear dynamics of the actuated fluidic pinball — Steady, periodic, and chaotic regimes

Thermal reaction norms depict how temperature influences biological performances, thus also known as thermal performance curves (TPCs). Arguably, the interplay of the thermal environment and the TPC can shape the strength of natural selection, thereby driving the long-term evolution of the TPC. We develop a Lotka-Volterra model, using adaptive dynamics (AD), to investigate how constant versus periodically fluctuating environmental temperatures drive the TPC adaptation. To formulate invasion fitness under fluctuating selection, we assume that the intrinsic rate of growth and carrying capacity to be temperature dependent, and also that the competition coefficient from one individual to another is proportional to the ratio of their beta-distribution-shaped thermal performances at the current environmental temperature. Results show that, under a constant temperature, the optimal temperature of the TPC evolves to align perfectly with the environmental temperature, with the TPC breadth shrinking to zero, reflecting local adaptation to complete thermal specialisation. In fluctuating thermal environments, adaptation produces broader TPCs, with their optimal temperature potentially mismatching the average environmental temperature. When the TPC’s optimal temperature matches the average temperature, large temperature fluctuations lead to broad TPCs (thermal generalisation). Our model also shows the emergence of bimodal TPCs under rapid and large temperature fluctuations, indicating adaptation to extreme temperatures and potentially a divergence of thermal strategies within the population. Our theoretical model has demonstrated that adaptation of TPCs in periodic thermal regimes promotes the evolution of thermal generalists and possible character divergence, compared to complete thermal specialisation in constant environments.

Controlled delay of regular, chaotic, and periodic regimes of instabilities is studied in the problem of axisymmetric Rayleigh–Bénard convection in a vertical cylinder. A feedback control is assumed at the boundaries, which leads to a coupling of the two boundary temperatures. A classical type solution is impossible in such a situation. Hence, a novel series solution procedure is adopted to arrive at the generalized Lorenz model. Due to feedback control, delayed onset of regular convection is observed and the percentage of such a delay as a function of the controller gain parameter, K, is reported. The changes in the pitchfork bifurcation point, the homoclinic orbit, and the Hopf bifurcation point due to feedback control are highlighted with the help of a bifurcation diagram. This diagram shows that the influence of feedback control is to advance the onset of homoclinic bifurcation and delay the onset of Hopf bifurcation. The results indicate that feedback control shows preference for Hopf bifurcation and is antagonistic toward homoclinic bifurcation. The shortening of the time of existence of the strange attractor intermittent with a periodic/quasi-periodic state, which is preceded by the fully periodic motion as K increases is observed using the largest-Lyapunov-exponent plot, the bar-code plot, and the bifurcation diagram. The results coming out of the Kaplan–Yorke dimension reiterates the results depicted by other indicators concerning the influence of K on chaos. The practical importance of the control strategy that is used in the paper is also mentioned in the paper.

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.

Spent mushroom substrate (SMS), often overlooked as waste despite its richness in organic matter and mineral micronutrients, is increasingly recognized as a versatile resource for various applications. This study examines the potential of SMS as a feedstock for biogas production. A periodic mesophilic fermentation regime at 36.0 ± 0.1°C was selected to conduct the experiments, after mixing the substrate with the inoculum, over a period of 38 days. The experimental results showed an average biogas yield of 292.7 Nm3/t of fresh SMS, with a methane concentration of 66.2%, making SMS a competitive resource for renewable energy production. This approach not only offers economic benefits for agricultural and energy sectors, but also supports environmental sustainability by promoting waste reduction and resource valorization.

In the Earth's atmosphere at the tropopause level, intense upper-tropospheric zonal flows are observed. To investigate the stability of these flows, a two-level discrete version of a surface quasigeostrophic (SQG) model is used. A nonlinear system of three differential equations for perturbation amplitudes is developed from the basic equations of this model using the Galerkin method. In the absence of Ekman friction, all solutions of the system describe a periodic regime of nonlinear oscillations or vacillations. The occurrence of such oscillations is determined by the law of conservation of the surface potential energy. In the dimensional variables, the period of oscillations is of the order of a month. This value agrees with the observed period of atmospheric oscillations in the winter period. A fundamentally new feature arises in the model taking into account the Ekman bottom friction. As in the classical Lorenz model, a regime of chaotic turbulent oscillations appears in the model with friction. This result confirms the main thesis of Lorenz – a model with three modes is sufficient to describe turbulence without involving cumbersome multi-mode models.

This study involves discretizing a continuous-time glycolysis model to derive its discrete-time equivalent and investigates its dynamics using normal form theory and bifurcation analysis. The discretization employs the forward Euler's scheme, and through rigorous analysis, we delve into codimension two bifurcations, with a specific focus on the 1:2, 1:3, and 1:4 strong resonances. The 1:2 resonance unveils intricate limit-cycle patterns, the 1:3 resonance reveals intriguing periodic solutions, and the 1:4 resonance showcases co-existing periodic and chaotic regimes. Our research sheds light on the complex behaviors of the discrete glycolysis model and provides valuable insights into its responses under varying parametric values. Additionally, this study demonstrates the applicability of normal form theory and bifurcation analysis in understanding the dynamics of biochemical systems, enriching our comprehension of the glycolysis process and its discrete dynamics. Moreover, we present numerical simulations to substantiate and validate our theoretical investigations. These simulations offer practical evidence and reinforce the findings obtained from the analytical study.

A finite volume technique-based in-house code is used for computational fluid dynamics (CFD) simulation and study on two-dimensional flow of fluid and transmission of thermal energy in a periodically fully developed sinusoidal serpentine channel with hydraulic diameter (Dh). This research activity is accomplished for various Reynolds number (Re = 101-2000) on three geometrically different serpentine channels for varying amplitude A ≡ a/D<sub>h</sub> = 0.1, 0.15, and 0.2 at constant wavelength λ* ≡ λ/D<sub>h</sub> = 1.5 of the wavy section. Unsteady flow regimes are characterized through the analysis of time signal plots, and a map is suggested for various flow regimes. The map demarcates steady regimes, both periodic and quasiperiodic regimes of two different types and a regime with chaotic flow at various governing parameters. The normalized ratio of the Nusselt number and that value of the friction coefficient for the serpentine wavy conduit with reference to the plane rectangular conduit are demonstrated to increase sharply in the unsteady regime with respect to the regime of steady flow. As Re increases, the value of goodness factor for the serpentine undulated conduit with respect to the plane rectangular conduit becomes almost constant for A = 0.15 and increases and decreases initially for A = 0.1 and 0.2, respectively, and thereafter remains almost constant. It was also found that the thermal performance factor (TPF) is more than one, suggesting that the gain in the transmission of thermal energy is greater than the pressure drop penalty in those flow regimes, where flow is unsteady for most of the Re. It was further noticed that the TPF increases with an increase in amplitude (A) from 0.1 to 0.15 and therefore remains constant for the increase in A from 0.15 to 0.2 at constant Re.

The aim of this work is to determine the conditions under which multistability is possible in system of three competing species described by reaction–diffusion–advection equations. Methods. Using the theory of cosymmetry and the concept of ideal free distribution, relations are established for the coefficients of local interaction, diffusion and directed migration, under which continuous families of solutions are possible. Compact scheme of the finite difference method is used to discretize the problem of species distribution on one-dimensional spatial area with periodicity conditions. Results. Conditions for parameters are found, under which stationary solutions proportional to the resource are obtained, corresponding to the ideal free distribution (IFD). The conditions under which two-parameter families of stationary distributions exist are studied. For parameters corresponding to IFD, family of periodic regimes is obtained in computational experiment. Conclusion. The obtained results demonstrate variants of multistability of species in resource-heterogeneous area and will further serve as a basis for the analysis of systems of interacting populations.