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The lowest fingerings of the saxophone can lead to several different regimes, depending on the musician’s control and the characteristics of the instrument. This is explored in this paper through a physical model of saxophone. The harmonic balance method shows that for many combinations of musician control parameters, several regimes are stable. Time-domain synthesis is used to show how different regimes can be selected through initial conditions and the initial evolution (rising time) of the blowing pressure, which is explained by studying the attraction basin of each stable regime. These considerations are then applied to study how the produced regimes are affected by properties of the resonator. The inharmonicity between the first two resonances is varied in order to find the value leading to the best suppression of unwanted overblowing. Overlooking multistability in this description can lead to biased conclusions. Results for all the lowest fingerings show that a slightly positive inharmonicity, close to that measured on a saxophone, leads to first register oscillations for the greatest range of control parameters. A perfect harmonicity (integer ratio between the first two resonances) decreases first register production, which adds nuance to one of Benade’s guidelines for understanding sound production. Thus, this study provides some a posteriori insight into empirical design choices relative to the saxophone.

The noise may drive the genetic toggle network switch from one stable state to another. To describe transcriptional bursting in synthesis process of biochemical systems, the Lévy noise is introduced to genetic toggle network with kinetic parameters and the dynamical transition is investigated via two deterministic quantities, the first escape probability and mean first exit time. Firstly, the analytical expressions of that two deterministic quantities in irregular domain are derived from the governing differential-integral equation. Then, the numerical schemes of the two indexes are developed by the finite difference method, and the validity of the proposed method is verified by the Monte Carlo simulations. Analyzing the Lévy noise on the switch mechine, we found that a decreasing stability index or an increasing noise intensity can reduce the probability of the first switching from the (low, high) state to the (high, low) state. Furthermore, higher noise intensity and stability index shorten the residence time of the (low, high) state.

In this paper, we examine the potential for coexisting responses in a harmonically forced buckled beam. It is shown experimentally that such structures may present many more responses than might be observed using frequency sweep-up and sweep-down testing, with some responses being observed only very infrequently. The primary contribution of this work is the experimental approximation of the basins of attraction of the competing behaviors using stochastic interrogation, which uses strong, but random, perturbations to map out the initial conditions that tend to each attractor. This procedure is especially difficult in experimental studies of distributed systems; hence, we focus on the process of stochastic interrogation itself and strictly in an experimental context.

How can the shape of biodiversity inform us about cities’ ecoclimatic fitness and guide their development? Can we use species as the harbingers of climatic extremes? Eco-climatically sensitive species carry information about hydroclimatic change in their distribution, fitness, and preferential gradients of habitat suitability. Conversely, environmental features outside of the species’ fitness convey information on potential ecological anomalies in response to extremes to adapt or mitigate, such as through urban parks. Here, to quantify ecosystems’ fitness, we propose a novel computational model to extract multivariate functional ecological networks and their basins, which carry the distributed signature of the compounding hydroclimatic pressures on sentinel species. Specifically, we consider butterflies and their habitat suitability (HS) to infer maximum suitability gradients that are meaningful of potential species networks and flows, with the smallest hydroclimatic resistance across urban landscapes. These flows are compared to the distribution of urban parks to identify parks’ ecological attractiveness, actual and potential connectivity, and park potential to reduce hydroclimatic impacts. The ecosystem fitness index (EFI) is novelly introduced by combining HS and the divergence of the relative species abundance (RSA) from the optimal log-normal Preston plot. In Shenzhen, as a case study, eco-flow networks are found to be spatially very extended, scale-free, and clustering for low HS gradient and EFI areas, where large water bodies act as sources of ecological corridors draining into urban parks. Conversely, parks with higher HS, HS gradients, and EFIs have small-world connectivity non-overlapping with hydrological networks. Diverging patterns of abundance and richness are inferred as increasing and decreasing with HS. HS is largely determined by temperature and precipitation of the coldest quarter and seasonality, which are critical hydrologic variables. Interestingly, a U-shape pattern is found between abundance and diversity, similar to the one in natural ecosystems. Additionally, both abundance and richness are mildly associated with park area according to a power function, unrelated to longitude but linked to the degree of urbanization or park centrality, counterintuitively. The Preston plot’s richness–abundance and abundance-rank patterns were verified to reflect the stationarity or ecological meta-equilibrium with the environment, where both are a reflection of community connectivity. Ecological fitness is grounded on the ecohydrological structure and flows where maximum HS gradients are indicative of the largest eco-changes like climate-driven species flows. These flows, as distributed stress-response functions, inform about the collective eco-fitness of communities, like parks in cities. Flow-based networks can serve as blueprints for designing ecotones that regulate key ecosystem functions, such as temperature and evapotranspiration, while generating cascading ecological benefits across scales. The proposed model, novelly infers HS eco-networks and calculates the EFI, is adaptable to diverse sensitive species and environmental layers, offering a robust tool for precise ecosystem assessment and design.

This work deals with the classical Job Shop Scheduling Problem (JSSP) of minimizing the makespan. Metaheuristics are often used on the JSSP solution, but a performance comparable to the state-of-the-art depends on an efficient exploration of the solutions space characteristics. Thus, it is proposed an intensification approach based on the concepts of attraction basins and big valley. Suboptimal solutions obtained by the metaheuristic genetic algorithm are selected and subjected to intensification, in which a binary Bidimensional Genetic Algorithm (BGA) is utilized to enlarge the search neighborhood from a current solution, to escape of attraction basins. Then, the best solution found in this neighborhood is used as the final point of the path relinking strategy derived from the initial suboptimal solution, for exploring possible big valleys. Finally, the best solution in the path is inserted into the population. Trials with usual instances of the literature show that the proposed approach yields greater results with regards to local search, based on permutation of operations on critical blocks, either on the makespan reduction or on the number of generations, and competitive results regarding the contemporary literature.

The paper proposes a mathematical model that describes mouse-like rodent population dynamics. The model is examined through analytical and numerical methods. Changes in the population parameter values lead to a complex evolution of dynamic regimes observed, namely periodic, quasi-periodic and chaotic oscillations, as well as changes in dynamic regimes caused by multistability and external factors. Multistability consists in the existence of various dynamic regimes under the same values of parameters; a transition to these regimes is determined by the initial conditions. An approach is proposed to study multistability by analysing annual population surveys and the model parameter estimates corresponding to the real data set, as well as environmental factors that influence both the birth rate and self-regulation. The adequacy of the results obtained is illustrated by comparing the simulations with the real dynamics of the bank vole population ( Myodes glareolus ) as a typical example of mouse-like rodents under non-constant environmental conditions. The model study shows that external factors lead to a significant change in attraction basins of coexisting dynamic regimes and shift in model parameter values over the parametric space, which results in a trajectory transition from one dynamic regime to another. As a result, the population size shifts between attraction basins of different dynamic regimes. In certain years, the population size can be attracted to an area of parameter values with similar regimes (the same period of cycles). In particular, the real dynamics of the bank vole population can be represented by a sequence of alternating transients that lead to fluctuations with 3-, 6-, 7- or 14-year periods under constant climatic conditions.

A new measure to characterize the stability of complex dynamical systems against large perturbations is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable of disrupting the system and switch it to an undesired dynamical regime. In the phase space, the ST corresponds to the 'thinnest site' of the attraction basin and therefore indicates the most 'dangerous' direction of perturbations. We introduce a computational algorithm for quantification of the ST and demonstrate that the suggested approach is effective and provides important insights. The generality of the obtained results defines their vast potential for application in such fields as engineering, neuroscience, power grids, Earth science and many others where the robustness of complex systems is studied.

This article introduces a multi-step solver for sets of nonlinear equations. To achieve this, we consider and develop a multi-step Steffensen-type method without memory, which does not require evaluations of the Fréchet derivatives, and subsequently extend it to a method with memory. The resulting order is 5+2, utilizing the identical number of functional evaluations as the solver without memory, thereby demonstrating a higher computational index of efficiency. Finally, we illustrate the advantages of the proposed scheme with memory through various test problems.

Chimera states-curious symmetry-broken states in systems of identical coupled oscillators-typically occur only for certain initial conditions. Here we analyze their basins of attraction in a simple system comprised of two populations. Using perturbative analysis and numerical simulation we evaluate asymptotic states and associated destination maps, and demonstrate that basins form a complex twisting structure in phase space. Understanding the basins' precise nature may help in the development of control methods to switch between chimera patterns, with possible technological and neural system applications.

This study focuses on the dynamics of exploited limited population with age structure and compares dynamic modes of population models with and without exploitation while considering age-specific harvesting. Transcritical, period-doubling, and Neimark–Sacker bifurcations occur in the population models. In the case of juvenile harvest, the way of stability loss does not depend on the harvest rate. However, in the case of adult harvest, the hydra effect occurs, which is an increase in harvest rate that subsequently increases the stationary size of the young group. As a rule, harvesting leads to dynamics stabilization. However, the models reveal multistability. Hence, in the case of exploitation, different dynamic modes can occur with their attraction basins at the same population parameter values. Irregular harvesting or a changing harvest rate may also result in fluctuations in exploited population size because the current population size can shift from one attraction basin to another. Controlling exploited population dynamics is sufficient to shift and retain the population number to within the attraction basin of the dynamic mode selected.