Synchronization of Vilnius Chaotic Oscillators With Active and Passive Control

Kocamaz, Uğur Erkin; Uyaroğlu, Yılmaz

doi:10.1142/s0218126614501035

Cited by 14 publications

(4 citation statements)

References 29 publications

(39 reference statements)

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“…First presented in 2004 [15], this circuit has been intended to become a tool to demonstrate the complex dynamics of simple electronic systems to students in the lab. Later, studies on the nonlinear dynamics of the oscillator and possible synchronization approaches have been provided [16,17]. However, the pronounced interest to the Vilnius oscillator has been shown since it has been adapted for practical IoT applications [18,19].…”

Section: Introductionmentioning

confidence: 99%

Complete Bifurcation Analysis of the Vilnius Chaotic Oscillator

et al. 2023

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The paper is dedicated to the numerical and experimental study of nonlinear oscillations exhibited by the Vilnius chaotic generator. The motivation for the work is defined by the need for a comprehensive analysis of the dynamics of the oscillators being embedded into chaotic communication systems. These generators should provide low-power operation while ensuring the robustness of the chaotic oscillations, insusceptible to parameter variations and noise. The work focuses on the investigation of the dependence of nonlinear dynamics of the Vilnius oscillator on the operating voltage and component parameter changes. The paper shows that the application of the Method of Complete Bifurcation Groups reveals the complex smooth and non-smooth bifurcation structures, forming regions of robust chaotic oscillations. The novel tool—mode transition graph—is presented, allowing the comparison of experimental and numerical results. The paper demonstrates the applicability of the Vilnius oscillator for the generation of robust chaos, and highlights the need for further investigation of the inherent trade-off between energy efficiency and robustness of the obtained oscillations.

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Section: Introductionmentioning

confidence: 99%

Complete Bifurcation Analysis of the Vilnius Chaotic Oscillator

et al. 2023

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“…Bifurcation analysis of the two saturated inductor resonant circuit has been discussed with a three dimensional Duffing type equation in [54] considering the system as a non-autonomous type. Some other well-known simplest chaotic oscillators are also discussed in the literatures like the Chuas oscillator [21], modified Wien bridge oscillator [27], simple 3D chaotic oscillator [31], Hartley oscillator [45], Vilnius oscillator [43], etc.…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Simple Chaotic Oscillator with Saturable Reactors and Its Engineering Applications

Rajagopal

Jafari

Kaçar

et al. 2019

ITC

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Chaos is often observed in forced nonlinear electrical circuits with saturable reactors. Simplest of such a circuit is presented and investigated in both integer order and non-integer (fractional) order form. For numerical analysis of fractional order system, the Adam-Bashforth-Moulton method is used. Some dynamic properties of the novel system are investigated. For implementing the system in field programmable gate arrays (FPGA), the Adomian decomposition method is used. Power and resource utilization of the fractional order system for implementing in FPGA are presented. Also, in this work, a novel fractional based sound encryption application is implemented as a unique application.

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“…In this paper, the method has been applied to certain nonlinear RLC circuit systems that are closely related to nonlinear oscillation [7], electronic theory (the differential equation of self-excited oscillation of an electronic triode [8]), and Lienard and Van der Pol equations. One can find some beautiful works in the literature discussing the stability (instability) behavior of circuit systems, such as Lyapunov stability for nonlinear descriptor systems [9], the global qualitative behavior of the double scroll system [10], chaos in the Colpitts oscillator due to positive Lyapunov exponents [11], unstable behavior of Hartley's oscillator because of the positive real parts of the eigenvalues of the Jacobian matrix of the system [12], and the global asymptotic stability (GAS) of the synchronization of Vilnius chaotic systems (using active and passive controls) determined by Lyapunov's direct method [13]. Moreover, some recent works have been done on the various behaviors of nonlinear RLC circuit systems: the existence of solutions [14], implicit solutions [15], power shaping [16], passivity and power-balance inequalities [17], and so on.…”

Section: Introductionmentioning

confidence: 99%

New results on the global asymptotic stability of certain nonlinear RLC circuits

Ateş¹,

Laribi²

2018

Turk J Elec Eng & Comp Sci

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This paper deals with the global asymptotic stability (GAS) of certain nonlinear RLC circuit systems using the direct Lyapunov method. For each system a suitable Lyapunov function or energy-like function is constructed and the direct Lyapunov method is applied to the related system. Then the invariant equilibrium point of each system that makes the system solution to the global asymptotic stable is determined. Some new explicit GAS conditions of certain nonlinear RLC circuit systems are derived by Lyapunov's direct method. The presented simulations are compatible with the new results. The results are given with proofs.

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Synchronization of Vilnius Chaotic Oscillators With Active and Passive Control

Cited by 14 publications

References 29 publications

Complete Bifurcation Analysis of the Vilnius Chaotic Oscillator

Complete Bifurcation Analysis of the Vilnius Chaotic Oscillator

Fractional Order Simple Chaotic Oscillator with Saturable Reactors and Its Engineering Applications

New results on the global asymptotic stability of certain nonlinear RLC circuits

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