Rich Dynamics Research Articles

Selection of the optimal design for a vibro-impact nonlinear energy sink

The efficiency of a vibro-impact nonlinear energy sink (VI NES), that is, a vibro-impact damper, is largely determined by its design. The optimal damper design can be found through optimization procedures. However, the result of their work is ambiguous, their various options show different values of the optimal damper parameters. A thorough analysis of the obtained parameters values allow you to select the best option according to a certain criterion. While carrying out this analysis, we observe many interesting phenomena, namely, the synergistic effect of multiple parameters, rich complex dynamics of the VI NES, the presence of direct impacts between the damper and the main body, the dependence of the total energy on the exciting force parameters.The analysis also allows us to formulate the limitations of the VI NES. All these problems are reflected in this article.

Heterogeneous encoding of temporal stimuli in the cerebellar cortex

Local feedforward and recurrent connectivity are rife in the frontal areas of the cerebral cortex, which gives rise to rich heterogeneous dynamics observed in such areas. Recently, similar local connectivity motifs have been discovered among Purkinje and molecular layer interneurons of the cerebellar cortex, however, task-related activity in these neurons has often been associated with relatively simple facilitation and suppression dynamics. Here, we show that the rodent cerebellar cortex supports heterogeneity in task-related neuronal activity at a scale similar to the cerebral cortex. We provide a computational model that inculcates recent anatomical insights into local microcircuit motifs to show the putative basis for such heterogeneity. We also use cell-type specific chronic viral lesions to establish the involvement of cerebellar lobules in associative learning behaviors. Functional heterogeneity in neuronal profiles may not merely be the remit of the associative cerebral cortex, similar principles may be at play in subcortical areas, even those with seemingly crystalline and homogenous cytoarchitectures like the cerebellum.

Modeling cooperative evolution in prey species using the snowdrift game with evolutionary impact on prey–predator dynamics

Cooperative evolution refers to the collaborative process by which two or more individuals or species interact and adapt together some specific behavior, leading to mutual benefits for their survival and reproduction. In this article, we employ the snowdrift game to model cooperative evolution in prey species and examine its evolutionary impact on the dynamics of prey–predator interactions. The model system consists of a replicator equation that captures the evolution of cooperative behavior in prey species, along with two growth equations of prey and predator incorporating the factors that influence cooperative evolution on prey reproduction. Our analysis reveals that in long time run, the prey population becomes polymorphic, allowing cooperative and defective individuals to coexist and persist over time. However, a very low cooperative proportion poses a risk of extinction for both prey and predator. Again if majority of prey species exhibit cooperative behavior, the predator species still faces possible extinction due to the strong group defense mechanism employed by prey. At some intermediate level of cooperative proportions, the proposed model system exhibits more rich and complex dynamics such as oscillatory patterns, bi-stable phenomena, homoclinic orbit, and saddle–node bifurcations of limit cycles. Further, we explore the transient dynamics of the proposed system through which one can anticipate the potential shifts in population size and can identify critical thresholds in promoting sustainable coexistence.

Coupled Nanomechanical Graphene Resonators: A Promising Platform for Scalable NEMS Networks.

Arrays of coupled nanoelectromechanical resonators are a promising foundation for implementing large-scale network applications, such as mechanical-based information processing and computing, but their practical realization remains an outstanding challenge. In this work, we demonstrate a scalable platform of suspended graphene resonators, such that neighboring resonators are persistently coupled mechanically. We provide evidence of strong coupling between neighboring resonators using two different tuning methods. Additionally, we provide evidence of inter-resonator coupling of higher-order modes, demonstrating the rich dynamics that can be accessed with this platform. Our results establish this platform as a viable option for realizing large-scale programmable networks, enabling applications such as phononic circuits, tunable waveguides, and reconfigurable metamaterials.

Spin Hall Switching Enabled by Uniaxial In-Plane Magnetocrystalline Anisotropy

We present a new method for stabilization of magnetic devices: in-plane uniaxial magnetocrystalline anisotropy, achieved through epitaxial growth of a magnetic thin film on a single-crystal substrate. This paradigm enables the creation of in-plane spin orbit torque magnetic random access memory (SOT-MRAM) devices that function without external fields and exhibit the same scalability as perpendicular SOT-MRAM. Through theoretical derivations and numerical simulations based on the Landau-Lifshitz-Gilbert (LLG) equation with spin transfer torque, we show that switching of such devices can be optimized by varying the angle between the injected spin current and the crystalline easy axis, and contrast this angular dependence with the Stoner-Wohlfarth model. Furthermore, we demonstrate rich and complex magnetization dynamics in this system, including strong and tunable dependence on bulk and interfacial magnetoresistance and boundaries between stochastic and deterministic switching. Finally, we present a concept that couples our in-plane anisotropy layer with an out-of-plane ferromagnet to achieve out-of-plane field-free SOT-MRAM switching. We quantify regions of operation for this new device and link them to simulation results for the in-plane layer alone.

Memristive Autapse-Coupled Neuron Model With External Electromagnetic Radiation Effects

Thanks to their distinct synaptic plasticity and memory effects, memristors not only can mimic biological neuronal synapses but also can describe the influence of external electromagnetic radiation. This paper proposes a novel memristive autapse-coupled neuron model (MACNM) using a locally active memristor as an autapse and simultaneously introducing a flux-controlled piecewise-nonlinear memristor to describe the external electromagnetic radiation. Theoretical analysis and numerical simulation results show that the MACNM is able to generate multiple numbers of grid multi-scroll hidden attractors. Moreover, it can exhibit rich and complex hidden firing dynamics, including periodic spiking/bursting firing, chaotic spiking/bursting firing as well as firing patterns transition. In particular, hidden firing multistability of five coexisting homogeneous chaotic bursting firing patterns with different offsets along the boosting route is discovered, giving raise to the interesting phenomenon of hidden homogeneous multistability. Finally, a circuit is designed to verify the physical feasibility of the abundant electrical activities in the proposed MACNM.

Deformation and destruction of north-eastward drifting dipoles

We systematically study the evolution of Larichev–Reznik dipoles in an equivalent-barotropic quasi-geostrophic beta-plane model in high-resolution numerical simulations. Our results shed light on the self-organization and rich dynamics of dipolar vortices, which are ubiquitous in geophysical flows. By varying both dipole strength and initial angle α0 of dipole tilt to the zonal direction, we discover new breakdown mechanisms of the dipole evolution. The dipoles are quickly destroyed by Rossby wave radiation, if initial tilt is too large or the dipole is too weak; otherwise, via damped oscillations, the dipoles tend to adjust themselves to different states drifting eastward. Two competing physical mechanisms that govern dipole transformations are found: (1) spontaneous dipole instability due to a growing critical linear mode and (2) meridional separation of dipole partners that accumulates over the adjustment period and prevents the above instability. Which mechanism prevails depends on the initial tilt and dipole strength, and the details of this are discussed.

Superposition of modulated nonlinear waves in inhomogeneous systems with negative coherent coupling

The superimposed wave solutions of the variable coefficient nonlinear Schrödinger equations with negative coherent coupling are derived under a more relaxed constraint condition than those in previous literatures. For the benefit of the more relaxed constraint, the dispersion, nonlinearity, and gain/loss can be designed freely, and the obtained solutions can describe the nonlinear waves in general inhomogeneous optical fiber systems. The obtained solutions with two free phase parameters can be deemed to be the superposition of the typical simple modulated solutions, and the arbitrary of the optical parameters and the free phase parameters be expected to give the rise of abundant forms of modulation functions, that leads to the diverse characteristics of superimposed waves. Take the kink dispersion fiber systems with constant gain/loss and trigonometric gain/loss as examples, rich dynamics of the superimposed waves are displayed. By changing the gain/loss, the physical features of superimposed waves, such as the amplitudes of solitons and Kuznetsov-Ma breathers, the widths of solitons, the distances between Kuznetsov-Ma breathers, and the backgrounds of Akhmediev breathers and rogue waves can be controlled. The interaction of solitons or Kuznetsov-Ma breathers, and the number of the rogue waves or Akhmediev breathers can also be manipulated by selecting appropriate value of gain/loss. The results presented here may be useful to explore the diverse dynamics of superimposed waves and prove significance for the control of nonlinear waves in weakly birefringent fibers.

Reservoir computing models based on spiking neural P systems for time series classification

Nonlinear spiking neural P (NSNP) systems are neural-like membrane computing models with nonlinear spiking mechanisms. Because of this nonlinear spiking mechanism, NSNP systems can show rich nonlinear dynamics. Reservoir computing (RC) is a novel recurrent neural network (RNN) and can overcome some shortcomings of traditional RNNs. Based on NSNP systems, we developed two RC variants for time series classification, RC-SNP and RC-RMS-SNP, which are without and integrated with reservoir model space (RMS), respectively. The two RC variants use NSNP systems as the reservoirs and can be easily implemented in the RC framework. The proposed two RC variants were evaluated on 17 benchmark time series classification datasets and compared with 16 state-of-the-art or baseline classification models. The comparison results demonstrate the effectiveness of the proposed two RC variants for time series classification tasks.

Experimental observation of stimulated Raman scattering enabled localized structure in a normal dispersion FP resonator

Dissipative Kerr nonlinear cavities attract intense interest due to their rich dynamics and capability to generate broadband, low-noise, mode-locked optical frequency combs for applications in optical communications, dual-comb spectroscopy, photonic lidar, etc. Different from the Kerr effect, which is an electronic response, stimulated Raman scattering (SRS) is a delayed response to molecular vibrations in materials. In microcavities, when driven in an anomalous group velocity dispersion (GVD) regime, SRS typically leads to a self-frequency shift of solitons and generation of breather solitons, which have been verified both theoretically and experimentally. However, when driven in a normal GVD regime, recent theoretical work predicts that SRS can cause the locking of switching waves (SWs) and thus support bright moving localized structure (LS), which we term as SRS enabled localized structure (SRS-LS). Limited by the design of suitable experimental parameters, experimental observation of this SRS-LS is not achieved yet. Here, we provide numerical investigation and, to our knowledge, the first experimental observation of the SRS-LS in a fiber Fabry–Perot (FP) resonator with ultra-low normal GVD. Such SRS-LS exhibits localized temporal features with strong oscillations at ∼13THz local frequency on the top of a flat-top pulse. The corresponding spectrum is a low-noise and broadband Kerr comb with a typical platicon-like spectrum in the center and two Raman Stokes and anti-Stokes peaks located near ±13THz away from the center. With such an SRS enabled broadband Kerr comb, we have achieved an SRS-LS spectrum with a repetition rate of ∼3.68GHz and a −30dB spectral width of 255 nm. The corresponding comb tooth count is >8500, covering the S + C + L telecommunication bands. Moreover, the formation process of such SRS-LS is also revealed, and it is found that the GVD plays a key role in its generation. Our work will help to advance the study of the dynamics of optical frequency combs under the influence of SRS, as well as provide a broadband coherent mode-locked optical source for wide applications.

Rich dynamics of a bidirectionally linked immuno-epidemiological model for cholera.

Cholera is an environmentally driven disease where the human hosts both ingest the pathogen from polluted environment and shed the pathogen to the environment, generating a two-way feedback cycle. In this paper, we propose a bidirectionally linked immuno-epidemiological model to study the interaction of within- and between-host cholera dynamics. We conduct a rigorous analysis for this multiscale model, with a focus on the stability and bifurcation properties of each feasible equilibrium. We find that the parameter that represents the bidirectional connection is a key factor in shaping the rich dynamics of the system, including the occurrence of the backward bifurcation and Hopf bifurcation. Numerical results illustrate a practical application of our model and add new insight into the prevention and intervention of cholera epidemics.

Geometric control of tilt transition dynamics in single-clamped thermalized elastic sheets.

We study the finite-temperature dynamics of thin elastic sheets in a single-clamped cantilever configuration. This system is known to exhibit a tilt transition at which the preferred mean plane of the sheet shifts from horizontal to a plane above or below the horizontal. The resultant thermally roughened two-state (up/down) system possesses rich dynamics on multiple timescales. In the tilted regime a finite-energy barrier separates the spontaneously chosen up state from the inversion-symmetric down state. Molecular dynamics simulations confirm that, over sufficiently long time, such thermalized elastic sheets transition between the two states, residing in each for a finite dwell time. One might expect that temperature is the primary driver for tilt inversion. We find, instead, that the primary control parameter, at fixed tilt order parameter, is the dimensionless and purely geometrical aspect ratio of the clamped width to the total length of the otherwise-free sheet. Using a combination of an effective mean-field theory and Kramers' theory, we derive the transition rate and examine its asymptotic behavior. At length scales beyond a material-dependent thermal length scale, renormalization of the elastic constants qualitatively modifies the temperature response. In particular, the transition is suppressed by thermal fluctuations, enhancing the robustness of the tilted state. We check and supplement these findings with further molecular dynamics simulations for a range of aspect ratios and temperatures.

Amplifying a Zeptonewton Force with a Single-Ion Nonlinear Oscillator.

Nonlinear mechanical resonators display rich and complex dynamics and are important in many areas of fundamental and applied sciences. Here, we present a general strategy to generate mechanical nonlinearities for trapped particles by transverse driving in a funnel-shaped potential. Employing a trapped ion platform, we study the nonlinear oscillation, bifurcation, and hysteresis of a single calcium ion and demonstrate a 20-fold enhancement of the signal from a zeptonewton-magnitude harmonic force through the effect of vibrational resonance. Our results represent a first step in combining the rich nonlinear dynamics with the precision control over mechanical motions offered by atomic physics and open up possibilities for exploiting nonlinear mechanical phenomena in the quantum regime.

Predicting discrete-time bifurcations with deep learning

Many natural and man-made systems are prone to critical transitions—abrupt and potentially devastating changes in dynamics. Deep learning classifiers can provide an early warning signal for critical transitions by learning generic features of bifurcations from large simulated training data sets. So far, classifiers have only been trained to predict continuous-time bifurcations, ignoring rich dynamics unique to discrete-time bifurcations. Here, we train a deep learning classifier to provide an early warning signal for the five local discrete-time bifurcations of codimension-one. We test the classifier on simulation data from discrete-time models used in physiology, economics and ecology, as well as experimental data of spontaneously beating chick-heart aggregates that undergo a period-doubling bifurcation. The classifier shows higher sensitivity and specificity than commonly used early warning signals under a wide range of noise intensities and rates of approach to the bifurcation. It also predicts the correct bifurcation in most cases, with particularly high accuracy for the period-doubling, Neimark-Sacker and fold bifurcations. Deep learning as a tool for bifurcation prediction is still in its nascence and has the potential to transform the way we monitor systems for critical transitions.

Coupling dynamics of dissipative localized structures: From polarized vector solitons to soliton molecules

Dissipative solitons are well known as representative nonlinear localized wave packets resulting from the composite balance of dispersion, nonlinearity, gain and loss in optical cavities. Since the last three decades, dissipative solitons keep as one of the most active research topics in the framework of nonlinear physics, not only for fundamental researches but also for various industrial applications. From one hand, due to the rich nonlinear dynamics, dissipative solitons have been considered as an ideal testbed to study the pumping-dissipation-bifurcation complexities. On the other hand, the emergences of dissipative solitons are tightly linked with the emission of ultrashort laser pulses, as well as the formation of broadband optical frequency combs. Compared with single-soliton counterpart, the multi-component dissipative solitons have exhibited even more fascinating properties and much wider range of applications, therefore the coupling dynamics of dissipative solitons is the blooming and emergent research area in the last decade. From this point of view, this review article covers the latest developments of compound dissipative solitons, not only in passive Kerr resonators, but also in mode-locked laser cavities. Ranging from polarized vector solitons to soliton molecules, the rising degree of freedom of these multi-component localized structures is boosting the discovery of novel nonlinear dynamics and underpin the various photonic applications in light science.

Complex networks for analyzing the urban acoustic environment

The urban acoustic environment (AE) provides comprehensive acoustic information related to the diverse systems of urban areas, such as traffic, the built environment, or biodiversity. The decreasing cost of acoustic sensors and rapid growth of storage space and computational power have fostered the collection of large amounts of acoustical data to be processed. However, despite the extensive information that is recorded by modern acoustic sensors, few approaches are established to capture the rich complex dynamics embedded in the time-frequency domain of the urban AE. Quantitative methods need to account for this complexity, while effectively reducing the high dimensionality of acoustic features within the data. Therefore, we introduce complex networks as a tool for analyzing the complex structure of large-scale urban AE data. We present a framework to construct networks based on frequency correlation matrices (FCMs). FCMs have shown to be a promising tool to depict environment specific interrelationships between consecutive power spectra. Accordingly, we show the capabilities of complex networks for the quantification of these interrelationships and thus, to characterize different urban AEs.We demonstrate the scope of the proposed method, using one of the world's most extensive longitudinal audio datasets, considering 3-min audio recordings (n = 319,385 ≙ 665 days) from 23 sites. We construct networks from hour-of-day specific audio recordings for each site. We show that the average shortest path length (ASPL) as an indicator for dominance of sound sources in the urban AE exhibits spatial- and temporal-specific patterns between the sites, which allows us to identify four to seven clusters of distinct urban AEs. To validate our findings, we use the land use mix around each site as a proxy for the AE and compare those between and within the clusters. The identified clusters show high intra- and low inter-cluster correlations of ASPL diel cycles as well as strong intra-similarities in land use mix. Our results indicate that complex networks are a promising approach to analyze large-scale audio data, expanding our understanding of the time-frequency domain of the urban AE.

Integrability and dynamics of a simplified class B laser system.

A simplified class B laser system is a family of differential polynomial systems of degree two depending on the parameters a and b. Its rich dynamics has already been observed in 1980s, see Arecchi et al. [Opt. Commun. 51, 308-314 (1984)] and Politi et al. [Phys. Rev. A 33, 4055 (1986)], and still nowadays, it attracts the interest of the researchers. In this paper, we characterize its dynamics near infinity for all values of the parameters. When a=0, the partial integrability was already proved by Oppo and Politi [Z. Phys. B Con. Mat. 59, 111-115 (1985)]. Here, we prove that for a=0, it is completely integrable with two independent first integrals given by Liouvillian functions, and we present a complete study of its dynamics. When a≠0, we study its dynamics in the Poincaré ball B3, i.e., the interior of this ball is identified with R3 and its boundary the two-dimensional sphere S2 is identified with the infinity of R3.

Impact of mini-hydropower on the chemical composition of water and phytoplankton of the reservoirs of the Forest-Steppe of Ukraine

The peculiarities of the transformation of river ecosystems in the reservoir at the construction of mini-hydropower plants have been found out. It was also found that the large-scale hydraulic engineering in the second half of the XX century caused significant changes in environmental conditions in the waterbodies, which has led to negative dynamics of species richness of aquatic organisms in general and phytoplankton in particular. Reservoir building has a significant negative impact on river ecosystems: currents slow down and disappear, canals become silted up, harmful substances of household and industrial waste gradually accumulate. The transformation of rivers into lake-type reservoirs is also accompanied by changes in the species composition and structure of phytoplankton. Eutrophication of reservoirs becomes typical. All this leads to significant degradation in aquatic ecosystems.

Optimal subradiant spin wave exchange in dipole-coupled atomic ring arrays

The subwavelength array of quantum emitters provides an ideal platform for exploring rich many-body dynamics, such as super- and subradiance. In this paper, we explore the dynamics of spin wave exchange between two dipole-coupled atomic ring arrays. Subradiant spin waves lead to low-loss and high efficiency of ring-to-ring transfer. The optimal subradiant spin wave exchange occurs at appropriate separations between coplanar rings, despite the fact that the energy transfer efficiency is monotonically enhanced (in the regime ) as the rings’ separation decreases. However, the spin wave will scatter due to the dephasing mechanism of close-by atom pairs, as the separation of two rings is too small. With the increase in the number of atoms on the ring, the subradiant shielding effect also strengthens, leading to a shorter distance for the transfer of spin waves. We investigate the rotation of one of the rings and find that the optimal spin wave exchange corresponds to the scenario where the line connecting the two nearest atoms of the two rings aligns with the center of the circle. Moreover, we study the influence of transition dipole moment orientations on the effective interaction between two atomic rings. We observe that there is a critical point where the effective interaction strength changes dramatically owing to the cooperative effect of the subwavelength atomic array. We believe that our results could be important for quantum information processing based on atomic arrays.

Oscillatory dynamics in a reaction network based on imine hydrolysis.

We have built an autocatalytic reaction network, based on the hydrolysis of certain imines, which exhibits bistability in an open system. The positive feedback originates from the interplay of fast acid-base equilibria, leading to hydroxide ion production, and pH-dependent hydrolysis rates. The addition of a first-order removal of the autocatalyst can result in sustained pH oscillations close to physiological conditions. The unit-amplitude pH oscillations are accompanied by the stoichiometric conversion of imine into amine back and forth. A systematic parameter search is carried out to characterize the rich observable dynamics and identify the evolving bifurcations.