•Presents a modified Chua’s circuit with three stable node-foci and two unstable saddles.•Hidden attractors have very small attraction basins not being connected with any fixed point.•Hidden ...attractors coexist with point attractors in the entire period-doubling bifurcation route.•Circuit simulations and DSP-assisted experiments validate the hidden attractors and multistability.
The first hidden chaotic attractor was discovered in a dimensionless piecewise-linear Chua’s system with a special Chua’s diode. But designing such physical Chua’s circuit is a challenging task due to the distinct slopes of Chua’s diode. In this paper, a modified Chua’s circuit is implemented using a 5-segment piecewise-linear Chua’s diode. In particular, the coexisting phenomena of hidden attractors and three point attractors are noticed in the entire period-doubling bifurcation route. Attraction basins of different coexisting attractors are explored. It is demonstrated that the hidden attractors have very small basins of attraction not being connected with any fixed point. The PSIM circuit simulations and DSP-assisted experiments are presented to illustrate the existence of hidden attractors and coexisting attractors.
The dynamical system without equilibrium point is considered having hidden dynamics. It is relatively difficult to locate the attractor in the state space as its attraction basin has nothing to do ...with the equilibrium point. Especially, generation of multi-scroll chaos from no-equilibrium system is a challenging task. In this paper, using sine function, a modified Sprott-A system without equilibrium point but with perpetual points is presented. In particular, this system has the conservative property of zero-sum Lyapunov exponents and thus can generate chaotic sea rather than an attractor. The locations of the scrolls of chaotic sea are found having potential relevance to the sine nonlinearities and perpetual points. Different number of scrolls can be extended only adjusting the system parameters. Three cases of five-term Sprott-A system variants with single-direction multi-scroll/multi-double-scroll chaotic sea and two-direction grid chaotic sea are demonstrated. Besides, hidden tori are found coexisting with the chaotic sea. Numerical simulations and hardware experiments both confirm the complex dynamics of the system.
•Variants of Sprott-A system without equilibrium.•Perpetual point of the no-equilibrium system.•Multi-scroll and grid-scroll conservative chaos.
Galactic cosmic rays consist of protons, electrons and ions, most of which are believed to be accelerated to relativistic speeds in supernova remnants. All components of the cosmic rays show an ...intensity that decreases as a power law with increasing energy (for example as E-2.7). Electrons in particular lose energy rapidly through synchrotron and inverse Compton processes, resulting in a relatively short lifetime (about 105 years) and a rapidly falling intensity, which raises the possibility of seeing the contribution from individual nearby sources (less than one kiloparsec away). Here we report an excess of galactic cosmic-ray electrons at energies of ∼300-800 GeV, which indicates a nearby source of energetic electrons. Such a source could be an unseen astrophysical object (such as a pulsar or micro-quasar) that accelerates electrons to those energies, or the electrons could arise from the annihilation of dark matter particles (such as a Kaluza-Klein particle with a mass of about 620 GeV).
During recent years it has been shown that hidden oscillations, whose basin of attraction does not overlap with small neighborhoods of equilibria, may significantly complicate simulation of dynamical ...models, lead to unreliable results and wrong conclusions, and cause serious damage in drilling systems, aircrafts control systems, electromechanical systems, and other applications. This article provides a survey of various phase-locked loop based circuits (used in satellite navigation systems, optical, and digital communication), where such difficulties take place in MATLAB and SPICE. Considered examples can be used for testing other phase-locked loop based circuits and simulation tools, and motivate the development and application of rigorous analytical methods for the global analysis of phase-locked loop based circuits.
Solar radio observations provide a unique diagnostic of the outer solar atmosphere. However, the inhomogeneous turbulent corona strongly affects the propagation of the emitted radio waves, so ...decoupling the intrinsic properties of the emitting source from the effects of radio wave propagation has long been a major challenge in solar physics. Here we report quantitative spatial and frequency characterization of solar radio burst fine structures observed with the Low Frequency Array, an instrument with high-time resolution that also permits imaging at scales much shorter than those corresponding to radio wave propagation in the corona. The observations demonstrate that radio wave propagation effects, and not the properties of the intrinsic emission source, dominate the observed spatial characteristics of radio burst images. These results permit more accurate estimates of source brightness temperatures, and open opportunities for quantitative study of the mechanisms that create the turbulent coronal medium through which the emitted radiation propagates.
The hidden oscillations (a basin of attraction of which does not contain neighborhoods of equilibria) have been obtained first in the 50–60s of the 20th century in automatic control systems with ...scalar piecewise-linear nonlinearity. This brings up the question about the excitation nature of hidden oscillations.
In the present paper it is shown that hidden oscillations can exist not only in systems with piecewise-linear nonlinearity but also in smooth systems. Here the possibility of the existence of a hidden chaotic attractor in a modified Chua’s system with a smooth characteristic of nonlinear element is demonstrated.
► There are hidden oscillations: basin does not contain neighborhoods of equilibria. ► Firstly hidden oscillations were found in systems with piecewise-linear nonlinearity. ► We show that hidden attractors can exist in systems with smooth nonlinearity. ► We suggest localization methods and find hidden attractors in a smooth Chua’s system.
The classical attractors of Lorenz, Rossler, Chua, Chen, and other widely-known attractors are those excited from unstable equilibria. From computational point of view this allows one to use ...numerical method, in which after transient process a trajectory, started from a point of unstable manifold in the neighborhood of equilibrium, reaches an attractor and identifies it. However there are attractors of another type:
hidden attractors, a basin of attraction of which does not contain neighborhoods of equilibria. In the present Letter for localization of hidden attractors of Chuaʼs circuit it is suggested to use a special analytical–numerical algorithm.
► There are hidden attractors: basin doesnʼt contain neighborhoods of equilibria. ► Hidden attractors cannot be reached by trajectory from neighborhoods of equilibria. ► We suggested special procedure for localization of hidden attractors. ► We discovered hidden attractor in Chuaʼs system, L. Chua in his work didnʼt expect this.
•The Lorenz-like system, describing rotating fluid convection is considered.•The scenario of transition to chaos in this system is described.•Analytical-numerical localization of hidden attractor in ...this system is demonstrated.
In this paper a Lorenz-like system, describing convective fluid motion in rotating cavity, is considered. It is shown numerically that this system, like the classical Lorenz system, possesses a homoclinic trajectory and a chaotic self-excited attractor. However, for the considered system, unlike the classical Lorenz system, along with self-excited attractor a hidden attractor can be localized. Analytical-numerical localization of hidden attractor is demonstrated.
A biosensor for the direct determination of organophosphorus pesticides (OPs) is described. It utilizes an ion‐selective field‐effect transistor and phosphotriesterase enzyme (PTE), which provides ...cleavage of OPs. The sensitivity of the biosensor was increased after PTE immobilization on the surface of the transistor. Packaging of the integrated circuit and creation of a microfluidic system for analyte delivery stabilized the signal. This system was able to detect 0.1 µM paraoxon and 0.5 µM parathion and methyl parathion and was stable for at least 1 month (PBS, 1°), and could thus provide the basis for a portable device for analyzing OPs in water.
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