We believe our strategy, which does not rely way too much on practical analysis considerations but more about analytic computations, would work to concrete situations arising in physics programs. Therefore, using this GK method of the Lyapunov coefficient as well as the SL regular form, the occurrence of Hopf bifurcations in the cloud-rain wait types of Koren and Feingold (KF) on one side and Koren, Tziperman, and Feingold on the other tend to be reviewed. Noteworthy may be the presence for the KF model of large parts of the parameter area which is why subcritical and supercritical Hopf bifurcations coexist. These areas are determined, in particular, by the intensity of the KF model’s nonlinear results. “Islands” of supercritical Hopf bifurcations tend to be shown to occur within a subcritical Hopf bifurcation “sea”; these islands being bordered by double-Hopf bifurcations occurring when the linearized dynamics during the critical equilibrium display two pairs of strictly imaginary eigenvalues.This paper proposes a simple no-equilibrium chaotic system with just one signum work as compared to the current no-equilibrium chaotic ones with a minumum of one quadratic or higher nonlinearity. The machine gets the offset boosting of three factors through adjusting the corresponding controlled constants. The ensuing hidden attractors is distributed in a 1D line, a 2D lattice, a 3D grid, and also in an arbitrary precise location of the phase room. Specifically, a hidden crazy bursting oscillation can be seen in this system, which will be an uncommon sensation. In addition, complex hidden characteristics is examined via phase portraits, time series Medial approach , Kaplan-Yorke dimensions, bifurcation diagrams, Lyapunov exponents, and two-parameter bifurcation diagrams. Then, a very simple hardware circuit without having any multiplier is fabricated, and also the experimental email address details are provided to demonstrate theoretical analyses and numerical simulations. Additionally, the randomness test for the crazy pseudo-random series generated by the system is tested by the National Institute of guidelines and Technology test room. The tested outcomes show that the suggested system has great randomness, hence becoming suitable for chaos-based applications such as for instance safe interaction and image encryption.We learn a heterogeneous population consisting of two groups of oscillatory elements, one with attractive and something with repulsive coupling. Moreover, we put different inner timescales when it comes to oscillators associated with the two groups and pay attention to the role of this timescale split within the collective behavior. Our outcomes display it may notably change synchronization properties for the system, and also the implications are fundamentally different with regards to the ratio involving the team timescales. When it comes to slower attractive group, synchronization properties act like the scenario of equal timescales. Nonetheless, if the appealing group is quicker, these properties somewhat change and bistability seems. One other collective regimes such as frozen states and individual states are shown to be crucially impacted by timescale separation.Shortcuts to adiabatic growth regarding the efficiently one-dimensional Bose-Einstein condensate (BEC) packed into the harmonic-oscillator (HO) pitfall are examined by combining techniques of variational approximation and inverse engineering. Piecewise-constant (discontinuous) advanced pitfall frequencies, like the understood bang-bang forms when you look at the optimal-control principle, derive from a defined answer of a generalized Ermakov equation. Control schemes considered when you look at the report include imaginary trap frequencies at short period of time scales, i.e., the HO potential replaced by the quadratic repulsive one. Using into respect the BEC’s intrinsic nonlinearity, email address details are reported when it comes to minimal transfer time, excitation power (which steps deviation through the effective adiabaticity), and stability for the shortcut-to-adiabaticity protocols. These answers are not just useful for the understanding of quick frictionless cooling, additionally help us to deal with fundamental dilemmas associated with the quantum rate restriction and thermodynamics.Large-scale nonlinear dynamical systems, such types of atmospheric hydrodynamics, chemical response systems, and electric circuits, often involve thousands or even more socializing components. So that you can identify crucial components when you look at the complex dynamical system along with to accelerate simulations, design decrease is frequently desirable. In this work, we develop an innovative new data-driven strategy using ℓ1-regularization for model reduced total of nonlinear dynamical systems, involving minimal parameterization and it has polynomial-time complexity, letting it easily deal with large-scale methods with up to 1000s of elements in a matter of minutes. A primary goal of our design reduction method is interpretability, that is to determine crucial the different parts of the dynamical system that play a role in behaviors of great interest, rather than just finding a competent projection of the dynamical system onto reduced proportions.