Constant-roll inflation in the generalized SU(2) Proca theory

The generalized SU(2) Proca theory (GSU2P for short) is a variant of the well known generalized Proca theory (GP for short) where the vector field belongs to the Lie algebra of the SU(2) group of global transformations under which the action is made invariant. New interesting possibilities arise in this framework because of the existence of new interactions of purely non-Abelian character and new configurations of the vector field that result in spatial spherical symmetry and the cosmological dynamics being driven by the propagating degrees of freedom. We study the two-dimensional phase space of the system that results when the cosmic triad configuration is employed in the Friedmann-Lemaitre-Robertson-Walker background and find an attractor curve whose attraction basin covers almost all the allowed region. Such an attractor curve corresponds to a primordial inflationary solution that has the following characteristic properties: 1.) it is a de Sitter solution whose Hubble parameter is regulated by a generalized version of the SU(2) group coupling constant, 2.) it is constant-roll including, as opposite limiting cases, the slow-roll and ultra slow-roll varieties, 3.) a number of e-folds $N > 60$ is easily reached, 4.) it has a graceful exit into a radiation dominated period powered by the canonical kinetic term of the vector field and the Einstein-Hilbert term. The free parameters of the action are chosen such that the tensor sector of the theory is the same as that of general relativity at least up to second-order perturbations, thereby avoiding the presence of ghost and Laplacian instabilities in the tensor sector as well as making the gravity waves propagate at light speed. This is a proof of concept of the interesting properties we could find in this scenario when the coupling constants be replaced by general coupling functions.

Lagrangian eddy tracking reveals the Eratosthenes anticyclonic attractor in the eastern Levantine Basin

Statistics of anticyclonic eddy activity and eddy trajectories in the Levantine Basin over the 2000–2018 period are analyzed using the DYNED-Atlas database, which links automated mesoscale eddy detection by the Angular Momentum Eddy Detection and Tracking Algorithm (AMEDA) algorithm to in situ oceanographic observations. This easternmost region of the Mediterranean Sea, delimited by the Levantine coast and Cyprus, has a complex eddying activity, which has not yet been fully characterized. In this paper, we use Lagrangian tracking to investigate the eddy fluxes and interactions between different subregions in this area. The anticyclonic structure above the Eratosthenes Seamount is identified as hosting an anticyclone attractor, constituted by a succession of long-lived anticyclones. It has a larger radius and is more persistent (staying in the same position for up to 4 years with successive merging events) than other eddies in this region. Quantification of anticyclone flux shows that anticyclones that drift towards the Eratosthenes Seamount are mainly formed along the Israeli coast or in a neighboring area west of the seamount. The southeastern Levantine area is isolated, with no anticyclone transfers to or from the western part of the basin, defining the effective attraction basin for the Eratosthenes anticyclone attractor. Co-localized in situ profiles inside eddies provide quantitative information on their subsurface physical anomaly signature, whose intensity can vary greatly with respect to the dynamical surface signature intensity. Despite interannual variability, the so-called Eratosthenes anticyclone attractor stores a larger amount of heat and salt than neighboring anticyclones, in a deeper subsurface anomaly that usually extends down to 500 m. This suggests that this attractor could concentrate heat and salt from this subbasin, which will impact the properties of intermediate water masses created there.

Two-Dimensional Manifolds of Modified Chen System with Time Delay

Two-dimensional unstable manifolds of the modified Chen system are constructed at equilibrium solution by “expanding up” along the unstable eigen-direction, hence it is tangent to the unstable eigenspace. In general, unstable manifold expands to the attraction basin of the corresponding limit cycle or attractor. With the introduction of time delay, the two-dimensional unstable manifold of an unstable focus is simulated via expanding solution orbits with restriction condition on the associated foliations. The simulated unstable manifold coincides with the attraction basin of the limit cycle of the delay differential equations.

A New 4D Piecewise Linear Multiscroll Chaotic System with Multistability and Its FPGA-Based Implementation

Due to the complex behavior of a multiscroll chaotic system, it is a good candidate for the secure communications. In this paper, by adding an additional variable to the modified Lorenz-type system, a new chaotic system that includes only linear and piecewise items but can generate 4n + 4 scroll chaotic attractors via choosing the various values of natural number n is proposed. Its dynamics including bifurcation, multistability, and symmetric coexisting attractors, as well as various chaotic and periodic behaviors, are analyzed by means of attraction basin, bifurcation diagram, dynamic map, phase portrait, Lyapunov exponent spectrum, and C0 complexity in detail. The mechanism of the occurrence for generating multiscroll chaotic attractors is presented. Finally, this multiscroll chaotic system is implemented by using the Altera Cyclone IV EP4CE10F17C8 FPGA. It is found that this FPGA-based design has an advantage of requiring less resources for 0% of the embedded multipliers and 0% of the PLLs of this FPGA are occupied.

ANÁLISE DA INTEGRIDADE E DA INSTABILIDADE DINÂMICA DE UM SISTEMA MECÂNICO SUJEITO A BIFURAÇÃO DO TIPO BUTTERFLY

Slender structural systems susceptible to unstable buckling generally losestability at lower load levels than the linear buckling load of the perfect structure. This is mainly due to the geometric imperfections present in real structures. The objective of this work is to determine the integrity measures, together with the stability of the post-critical solutions of a mechanical system subject to unstable symmetrical buckling, Burtterfly-type bifurcation, using a discrete degree of freedom model. Uncertainties in the order of 10% will be considered in its deterministic parameters, to obtain lower and reliable limits for the project. The proposed uncertainty in the spring stiffness parameters does not change the type of bifurcation and the value of the critical load, only the value of the minimum post-critical of the bifurcation diagrams. The results showed the erosion of the attraction basin and the decrease of the factors of integrity, local and global, for the trivial solutions with the increase of the static load, for the investigated bifurcation.

Multistability of saxophone oscillation regimes and its influence on sound production

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.

A New Four-Dimensional Non-Hamiltonian Conservative Hyperchaotic System

This paper presents a new four-dimensional non-Hamiltonian conservative hyperchaotic system. In the absence of equilibrium points in the system, the phase trajectories generated by the system have hidden features. The conservative features that vary with the parameter have been analyzed in detail by Lyapunov exponent spectrum, bifurcation diagram, the sum of Lyapunov exponents, and the fractional dimensions, and during the analysis, multiple quasi-periodic four-dimensional tori as well as hyperchaotic attractors have been observed. The Poincaré sections confirm these dynamic behaviors. Amidst the process of studying the dynamical behavior of the system with initial values, the hidden extreme multistability, and the initial offset boosting behavior, the results have been witnessed for the very first time in a conservative chaotic system. The phase diagram and attraction basin also confirm this assertion, while two complex transient transition behaviors have been observed. Moreover, through the introduction of a spectral entropy algorithm, the complexity analysis of the time sequences generated by the system have been performed and compared with the existing literature. The results show that the system has a high degree of complexity. The design and construction of the analog circuit of the system for simulation, the circuit experimental results are consistent with the numerical simulation, further verifying the physical realizability of the newly proposed system. This lays a good foundation for its practical application in engineering.

Statistics of Lifetimes for Transient Bursting States in Coupled Noisy Excitable Systems

In ensembles of oscillators, intrinsic fluctuations often enable nontrivial dynamics in seemingly simple situations. One of such effects occurs in coupled FitzHugh–Nagumo oscillators subjected to external noise. At the considered parameter values, the global deterministic attractor is the resting state. Additive noise invokes transient bursting: series of intermittent patches of spikes, followed by the abrupt decay to rest. Duration of this transient, small for weak noise, asymptotically diverges when the noise becomes stronger. Remarkably, in repeated trials at fixed parameters, the number of bursts until the ultimate decay strongly varies. Lifetime statistics for this transient in large ensembles of numerical realizations features the exponential distribution. Observations on transient bursting are confirmed by experiments with coupled analog electronic circuits, modeling the FitzHugh–Nagumo dynamics. We relate the exponential character of the distribution to the probability that the system, disturbed by noise, escapes the local attraction basin of the resting state.

Four-Wing Hidden Attractors with One Stable Equilibrium Point

Although multiwing hidden attractor chaotic systems have attracted a lot of interest, the currently reported multiwing hidden attractor chaotic systems are either with no equilibrium point or with an infinite number of equilibrium points. The multiwing hidden attractor chaotic systems with stable equilibrium points have not been reported. This paper reports a four-wing hidden attractor chaotic system, which has only one stable node-focus equilibrium point. The novel system can also generate a hidden attractor with one-wing and hidden attractors with quasi-periodic and periodic coexistence. In addition, a self-excited attractor with one-wing can be generated by adjusting the parameters of the novel system. The hidden attractors of the novel system are verified by the cross-section of attraction basins. And the hidden behavior is investigated by choosing different initial states. Moreover, the coexisting transient four-wing phenomenon of the self-excited one-wing attractor system is studied by the time domain waveforms and attraction basin. The dynamical characteristics of the novel system are studied by Lyapunov exponents spectrum, bifurcation diagram and Poincaré map. Furthermore, the novel hidden attractor system with four-wing and one-wing are implemented by electronic circuits. The hardware experiment results are consistent with the numerical simulations.

Steering eco-evolutionary game dynamics with manifold control

Feedback loops between population dynamics of individuals and their ecological environment are ubiquitously found in nature and have shown profound effects on the resulting eco-evolutionary dynamics. By incorporating linear environmental feedback law into the replicator dynamics of two-player games, recent theoretical studies have shed light on understanding the oscillating dynamics of the social dilemma. However, the detailed effects of more general nonlinear feedback loops in multi-player games, which are more common especially in microbial systems, remain unclear. Here, we focus on ecological public goods games with environmental feedbacks driven by a nonlinear selection gradient. Unlike previous models, multiple segments of stable and unstable equilibrium manifolds can emerge from the population dynamical systems. We find that a larger relative asymmetrical feedback speed for group interactions centred on cooperators not only accelerates the convergence of stable manifolds but also increases the attraction basin of these stable manifolds. Furthermore, our work offers an innovative manifold control approach: by designing appropriate switching control laws, we are able to steer the eco-evolutionary dynamics to any desired population state. Our mathematical framework is an important generalization and complement to coevolutionary game dynamics, and also fills the theoretical gap in guiding the widespread problem of population state control in microbial experiments.