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Chaos in the Colpitts oscillator
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TLDR
In this article, the authors present experimental results and SPICE simulations of chaos in a Colpitts oscillator and show that the nonlinear dynamics of this oscillator may be modeled by a third-order autonomous continuous-time circuit consisting of a linear inductor, two linear capacitors, 2 linear resistors, two independent voltage sources, a linear current-controlled current source, and a single voltage-controlled nonlinear resistor.Abstract:
In this work, we present experimental results and SPICE simulations of chaos in a Colpitts oscillator. We show that the nonlinear dynamics of this oscillator may be modeled by a third-order autonomous continuous-time circuit consisting of a linear inductor, two linear capacitors, two linear resistors, two independent voltage sources, a linear current-controlled current source, and a single voltage-controlled nonlinear resistor. The nonlinear resistor has a two-segment piecewise-linear DP characteristic. With the appropriate choice of parameters, the piecewise-linear circuit model has a positive Lyapunov exponent. >read more
Citations
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Construction of classes of circuit-independent chaotic oscillators using passive-only nonlinear devices
TL;DR: In this paper, two generic classes of chaotic oscillators comprising four different configurations are constructed based on the simplest possible abstract models of generic second-order RC sinusoidal oscillators that satisfy the basic condition for oscillation and the frequency of oscillation formulas.
Journal ArticleDOI
Bifurcation Sets of Continuous Piecewise Linear Systems with Two Zones
TL;DR: In this paper, a canonical form which captures the most interesting oscillatory behavior is obtained and their bifurcation sets are drawn, and different mechanisms for the creation of periodic orbits are detected, and their main characteristics are emphasized.
Journal ArticleDOI
Nonlinear analysis of the Colpitts oscillator and applications to design
TL;DR: A methodological approach to the analysis and design of sinusoidal oscillators based on bifurcation analysis is reported, showing how regular and irregular oscillations can be generated, depending on the circuit parameters.
Journal ArticleDOI
A New Chaotic Jerk Circuit
TL;DR: This paper describes a particularly elegant circuit whose operation is accurately described by a simple variant of that equation in which the requisite nonlinearity is provided by a single diode and for which the analysis is particularly straightforward.
Journal ArticleDOI
Three Types of Transitions to Phase Synchronization in Coupled Chaotic Oscillators
TL;DR: Depending on the coherence properties of oscillations characterized by the phase diffusion, three types of transitions to phase synchronization are found, including phase locking, phase locking and phase synchronization sets in via an interior crises of the hyperchaotic set.
References
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Journal ArticleDOI
Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua's circuits
TL;DR: In this article, a technique for transmitting digital information using a chaotic carrier is described, in which each symbol to be transmitted is coded as an attractor in Chua's circuit.
Journal ArticleDOI
Transmission of digital signals by chaotic synchronization
TL;DR: The transmission of digital signals by means of chaotic synchronization is demonstrated, numerically as well as experimentally, via Chua’s circuit.
Proceedings ArticleDOI
Signal processing in the context of chaotic signals
TL;DR: A variety of signal processing issues associated with the analysis and synthesis of chaotic signals are outlined and two examples are described in detail, illustrating some possible ways in which the characteristics of chaos signals and systems can be exploited.
Journal ArticleDOI
INSITE—A software toolkit for the analysis of nonlinear dynamical systems
T.S. Parker,Leon O. Chua +1 more
TL;DR: An integrated software toolkit for the analysis of nonlinear dynamical systems is introduced, which includes software that calculates and displays trajectories, bifurcation diagrams, and two-dimensional phase portraits.