35 research outputs found
Rich Variety of Bifurcations and Chaos in a Variant of Murali-Lakshmanan-Chua Circuit
A very simple nonlinear parallel nonautonomous LCR circuit with Chua's diode
as its only nonlinear element, exhibiting a rich variety of dynamical features,
is proposed as a variant of the simplest nonlinear nonautonomous circuit
introduced by Murali, Lakshmanan and Chua(MLC). By constructing a two-parameter
phase diagram in the plane, corresponding to the forcing amplitude
(F) and frequency , we identify, besides the familiar period-doubling
scenario to chaos, intermittent and quasiperiodic routes to chaos as well as
period-adding sequences, Farey sequences, and so on. The chaotic dynamics is
verified by both experimental as well as computer simulation studies including
PSPICE.Comment: 4 pages, RevTeX 4, 5 EPS figure
Bubbling route to strange nonchaotic attractor in a nonlinear series LCR circuit with a nonsinusoidal force
We identify a novel route to the birth of a strange nonchaotic attractor
(SNA) in a quasiperiodically forced electronic circuit with a nonsinusoidal
(square wave) force as one of the quasiperiodic forces through numerical and
experimental studies. We find that bubbles appear in the strands of the
quasiperiodic attractor due to the instability induced by the additional square
wave type force. The bubbles then enlarge and get increasingly wrinkled as a
function of the control parameter. Finally, the bubbles get extremely wrinkled
(while the remaining parts of the strands of the torus remain largely
unaffected) resulting in the birth of the SNA which we term as the
\emph{bubbling route to SNA}. We characterize and confirm this birth from both
experimental and numerical data by maximal Lyapunov exponents and their
variance, Poincar\'e maps, Fourier amplitude spectra and spectral distribution
function. We also strongly confirm the birth of SNA via the bubbling route by
the distribution of the finite-time Lyapunov exponents.Comment: 11 pages. 11 figures, Accepted for publication in Phys. Rev.
Experimental realization of strange nonchaotic attractors in a quasiperiodically forced electronic circuit
We have identified the three prominent routes, namely Heagy-Hammel,
fractalization and intermittency routes, and their mechanisms for the birth of
strange nonchaotic attractors (SNAs) in a quasiperiodically forced electronic
system constructed using a negative conductance series LCR circuit with a diode
both numerically and experimentally. The birth of SNAs by these three routes is
verified from both experimental and their corresponding numerical data by
maximal Lyapunov exponents, and their variance, Poincar\'e maps, Fourier
amplitude spectrum, spectral distribution function and finite-time Lyapunov
exponents. Although these three routes have been identified numerically in
different dynamical systems, the experimental observation of all these
mechanisms is reported for the first time to our knowledge and that too in a
single second order electronic circuit.Comment: 21 figure
Experimental evidence for vibrational resonance and enhanced signal transmission in Chua's circuit
We consider a single Chua's circuit and a system of a unidirectionally
coupled n-Chua's circuits driven by a biharmonic signal with two widely
different frequencies \omega and \Omega, where \Omega >> \omega. We show
experimental evidence for vibrational resonance in the single Chua's circuit
and undamped signal propagation of a low-frequency signal in the system of
n-coupled Chua's circuits where only the first circuit is driven by the
biharmonic signal. In the single circuit, we illustrate the mechanism of
vibrational resonance and the influence of the biharmonic signal parameters on
the resonance. In the n(= 75)-coupled Chua's circuits enhanced propagation of
low-frequency signal is found to occur for a wide range of values of the
amplitude of the high-frequency input signal and coupling parameter. The
response amplitude of the ith circuit increases with i and attains a
saturation. Moreover, the unidirectional coupling is found to act as a low-pass
filter.Comment: 15 pages, 12 figures, Accepted for Publication in International
Journal of Bifurcation and Chao
Effect of Sintering Temperature on Metal-Insulator Phase Transition in La1-xCaxMnO3 Perovskites
Lanthanum calcium based perovskites are found to be advantageous for the possible applications in magnetic sensors/reading heads, cathodes in solid oxide fuel cells, and frequency switching devices. In the present investigation La0.3Ca0.7MnO3 perovskites were synthesised through solid state reaction and sintered at four different temperatures such as 900, 1000, 1100 and 1200˚ C. X-ray powder diffraction pattern confirms that the prepared La0.3Ca0.7MnO3 perovskites have orthorhombic structure with Pnma space group. Ultrasonic in-situ measurements have been carried out on the La0.3Ca0.7MnO3 perovskites over wide range of temperature and elastic constants such as bulk modulus of the prepared La0.3Ca0.7MnO3 perovskites was obtained as function of temperature. The temperature-dependent bulk modulus has shown an interesting anomaly at the metal-insulator phase transition. The metal insulator transition temperature derived from temperature-dependent bulk modulus increases from temperature 352˚ C to 367˚ C with the increase of sintering temperature from 900 to 1200˚ C
Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators
D.V.S. was supported by the SERB-DST Fast Track scheme for young scientist under Grant No. ST/FTP/PS-119/2013. K.S. acknowledges the DST, India, and the Bharathidasan University for financial support under the DST-PURSE programme. The work of V.K.C. was supported by the INSA young scientist project. W.Z. acknowledges the financial support from the National Natural Science Foundation of China under Grant No. 11202082. K.T. acknowledges the DST, India, for financial support. S.K.D. was supported by the CSIR Emeritus scientist schemePeer reviewedPublisher PD
CLASSIFICATION OF BIFURCATIONS AND ROUTES TO CHAOS IN A VARIANT OF MURALI LAKSHMANAN CHUA CIRCUIT
We present a detailed investigation of the rich variety of bifurcations and chaos associated with a very simple nonlinear parallel nonautonomous LCR circuit with Chua’s diode as its only nonlinear element as briefly reported recently [Thamilmaran et al., 2000]. It is proposed as a variant of the simplest nonlinear nonautonomous circuit introduced by Murali, Lakshmanan and Chua (MLC) [Murali et al., 1994]. In our study we have constructed two-parameter phase diagrams in the forcing amplitude-frequency plane, both numerically and experimentally. We point out that under the influence of a periodic excitation a rich variety of bifurcation phenomena, including the familiar period-doubling sequence, intermittent and quasiperiodic routes to chaos as well as period-adding sequences, occur. In addition, we have also observed that the periods of many windows satisfy the familiar Farey sequence. Further, reverse bifurcations, antimonotonicity, remerging chaotic band attractors, and so on, also occur in this system. Numerical simulation results using Poincaré section, Lyapunov exponents, bifurcation diagrams and phase trajectories are found to be in agreement with experimental observations. The chaotic dynamics of this circuit is observed experimentally and confirmed both by numerical and analytical studies as well PSPICE simulation results. The results are also compared with the dynamics of the original MLC circuit with reference to the two-parameter space to show the richness of the present circuit
Hyperchaos in a modified canonical Chua's circuit
In this paper, we present the hyperchaos dynamics of a modified canonical Chua's electrical circuit. This circuit, which is capable of realizing the behavior of every member of the Chua's family, consists of just five linear elements (resistors, inductors and capacitors), a negative conductor and a piecewise linear resistor. The route followed is a transition from regular behavior to chaos and then to hyperchaos through border-collision bifurcation, as the system parameter is varied. The hyperchaos dynamics, characterized by two positive Lyapunov exponents, is described by a set of four coupled first-order ordinary d.3.
ifferential equations. This has been investigated extensively using laboratory experiments, P spice simulation and numerical analysis