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Polynomial functions have been the main barrier restricting the circuit realization and engineering application of multiwing chaotic systems (MWCSs). To eliminate this bottleneck, we construct a simple MWCS without polynomial functions by introducing a sinusoidal function in a Sprott C system. Theoretical analysis and numerical simulations show that the MWCS can not only generate multibutterfly attractors with an arbitrary number of butterflies, but also adjust the number of the butterflies by multiple ways including self-oscillating time, control parameters, and initial states. To further explore the advantage of the proposed MWCS, we realize its analog circuit using commercially available electronic elements. The results demonstrate that in comparison to traditional MWCSs, our circuit implementation greatly reduces the consumption of electronic components. This makes the MWCS more suitable for many chaos-based engineering applications. Furthermore, we propose an application of the MWCS to chaotic image encryption. Histogram, correlation, information entropy, and key sensitivity show that the simple image encryption scheme has a high security and reliable encryption performance. Finally, we develop a field-programmable gate array test platform to implement the MWCS-based image cryptosystem. Both theoretical analysis and experimental results verify the feasibility and availability of the proposed MWCS. [ABSTRACT FROM AUTHOR]

This brief proposes a simple autonomous chaotic circuit based on minimum discrete component implementation. First, the circuit employs only five discrete components, including one op-amp, one resistor, one inductor, and two capacitors. Second, the circuit equations have six linear terms and one invariant dead-zone nonlinearity. Third, the circuit is robust stand-alone and has the most common implementation. The comprehensive dynamical behaviors are analyzed by using two-parameter bifurcation diagrams, Lyapunov exponents, and phase plots. The experimental demonstrations validated the analyses. [ABSTRACT FROM AUTHOR]

We introduce in this paper an equivalence notion for submersions U → ℝ , U open in ℝ 2 , which makes it possible to identify a smooth planar curve with a unique class of submersions. This idea, which extends to the nonlinear setting the construction of a dual projective space, provides a systematic way to handle global implicit descriptions of smooth planar curves. We then apply this framework to model nonlinear electrical devices as classes of equivalent functions. In this setting, linearization naturally accommodates incremental resistances (and other analogous notions) in homogeneous terms. This approach, combined with a projectively-weighted version of the matrix-tree theorem, makes it possible to formulate and address in great generality several problems in nonlinear circuit theory. In particular, we tackle unique solvability problems in resistive circuits, and discuss a general expression for the characteristic polynomial of dynamic circuits at equilibria. Previously known results, which were derived in the literature under unnecessarily restrictive working assumptions, are simply obtained here by using dehomogenization. Our results are shown to apply also to circuits with memristors. We finally present a detailed, graph-theoretic study of certain stationary bifurcations in nonlinear circuits using the formalism here introduced. [ABSTRACT FROM AUTHOR]

A novel 4-D hyperchaotic four-wing system with a saddle–focus equilibrium is introduced in this brief. The qualitative analysis of the proposed system confirms its complex dynamic behavior, which is studied by using well-known numerical tools of nonlinear theory, such as the bifurcation diagram, Lyapunov exponents, Poincaré maps, and phase portraits. Furthermore, the novel hyperchaotic system is experimentally emulated by an electronic circuit, and its dynamic behavior is studied to confirm the feasibility of the theoretical model. [ABSTRACT FROM PUBLISHER]

This paper presents a comprehensive taxonomy of so-called second-order memory devices, which include charge-controlled memcapacitors and flux-controlled meminductors, among other novel circuit elements. These devices, which are classified according to their differential and state orders, are necessary to get a complete extension of the family of classical nonlinear circuit elements (resistors, capacitors, and inductors) for all possible controlling variables. Using a fully nonlinear formalism, we obtain nondegeneracy conditions for a broad class of second-order mem-circuits. This class of circuits is expected to yield a rich dynamic behavior; in this regard, we explore certain bifurcation phenomena exhibited by a family of circuits including a charge-controlled memcapacitor and a flux-controlled meminductor, providing some directions for future research. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The paper presents an analytical and numerical investigation carried out on part of an electrical power network exhibiting ferroresonant behaviour as well as experimental investigation on its physical model. The investigations were carried out in order to estimate the extent of predicting the range of voltage source amplitude values at which the initiation of ferroresonance depends on values of initial conditions and phase shift. For this range of voltage source amplitude values (termed as possible ferroresonant range in the paper), the impact of initial conditions and phase shift of voltage source on the initiation of ferroresonance is determined using a numerical investigation and an experimental set-up. Reasons and consequences of disagreement of parameter values of the original and physical model are determined. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this report the dynamic behaviour of a nonlinear finance chaotic system was modeled by an electronic circuit and its behaviour was studied by means of electronic circuit simulation tools. A recently new proposed finance system is used. For this reason, a totally different approach in the study of its dynamic behaviour by using the bifurcation diagram is followed, in regard to previous work. The numerical tools of this approach were not only the bifurcation diagram, but also the maximum Lyapunov exponents and the phase portraits. Various phenomena concerning the chaos theory, such as the route to chaos through the mechanism of period doubling, internal and boundary crisis and the coexistence of attractors, were observed. [ABSTRACT FROM AUTHOR]

The forced Rayleigh equation is known as the differential equation for which the existence of the aperiodic solution is shown for the first time, From the viewpoint of the history of the research of chaos, it is very important to examine the bifurcation in this equation. The authors considered the forced Rayleigh oscillator containing a diode. By considering the limit α → ∞ for a parameter α contained in the system, the ideal diode constrained equation is defined. Then, the rigorous analysis of the bifurcation phenomenon is made for the forced Rayleigh oscillator. This paper considers the forced Rayleigh oscillator containing a large parameter α and shows that the bifurcation concerning the chaos generated in the oscillator can be accounted for by the ideal diode constrained equation by constructing and comparing the detailed bifurcation diagrams for the two systems. [ABSTRACT FROM AUTHOR]

The forced Rayleigh equation is known to be the first differential equation for which the aperiodic oscillation is shown to exist. For this type of equation, however, it is not known whether chaos exists and neither has any detailed study been made on the bifurcation phenomenon. With this as background, the authors have repotted [1, 2] that a chaotic oscillation can exist in the forced Rayleigh equation. In [1] and [2], the authors accounted for the generation of chaos by regarding the nonlinear element as strongly dissipative (α→∞) and deriving the constrained equation so that the Poincaré map corresponds to the noninvertible circle map. In this paper, the forementioned constrained equation is used to analyze the bifurcation phenomenon in the forced Rayleigh equation. Interesting phenomena are verified, such as Arnold tongue, intermittency, period-doubling bifurcation and phase-locked chaos, which are accounted for by the forementioned mapping. It is shown especially that the transition to the torus and the intermittency can clearly be distinguished when the tangent bifurcation is generated. The Lyapunov exponent is calculated for the constrained equation and the case where α is finite, and it is verified numerically that the Lyapunov exponent converges to that of the constrained equation when α → ∞. [ABSTRACT FROM AUTHOR]