Homoclinic bifurcation in Chua’s circuit

Dana, Syamal K.; Chakraborty, Satyabrata; Ananthakrishna, G.

doi:10.1007/bf02704570

Cited by 30 publications

(8 citation statements)

References 23 publications

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“…The time spent during spiraling out varies and it depends on how close the reinjected trajectory reaches a vicinity of the saddle focus and thereby it makes a large variation in the number of small oscillations that makes irregular return time of the large events. A tendency to develop a homoclinic chaos with a local instability of the saddle focus is seen here, but the typical global stability of homoclinic chaos [39] is never achieved due to the presence of a channel like structure. The trajectory revolves around the saddle focus for quite some time due to local instability (attracted along the stable eigendirection, pushed away along the unstable eigenplane of the saddle focus) while a globally instability due to the channel-like structure induces a variation of the return path (global excursion) of the trajectory making a wide variation in both the amplitude and return time of large spikes.…”

Section: Complex Dynamics Of Enso Modelmentioning

confidence: 67%

Understanding the origin of extreme events in El Niño-Southern Oscillation

Ray,

Rakshit,

Basak

et al. 2020

Preprint

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We investigate a low-dimensional slow-fast model to understand the dynamical origin of El Niño-Southern Oscillation. A close inspection of the system dynamics using several bifurcation plots reveals that a sudden large expansion of the attractor occurs at a critical system parameter via a type of interior crisis. This interior crisis evolves through merging of a cascade of period-doubling and period-adding bifurcations that leads to the origin of occasional amplitude-modulated extremely large events. More categorically, a situation similar to homoclinic chaos arises near the critical point, however, atypical global instability evolves as a channel-like structure in phase space of the system that modulates variability of amplitude and return time of the occasional large events and makes a difference from the homoclinic chaos. The slow-fast timescale of the low-dimensional model plays an important role on the onset of occasional extremely large events. Such extreme events are characterized by their heights when they exceed a threshold level measured by a meanexcess function. The probability density of events' height displays multimodal distribution with an upper-bounded tail. We identify the dependence structure of interevent intervals to understand the predictability of return time of such extreme events using autoregressive integrated moving average model and box plot analysis.

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Section: Complex Dynamics Of Enso Modelmentioning

confidence: 67%

Understanding the origin of extreme events in El Niño-Southern Oscillation

Ray,

Rakshit,

Basak

et al. 2020

Preprint

View full text Add to dashboard Cite

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“…fundamental features of spiking and bursting in a neuron. Bursting is also observed in physical systems like CO 2 lasers [12], an asymmetric Chua oscillator [13] and forced Josephson junctions [14].…”

Section: Introductionmentioning

confidence: 93%

Bursting Near Homoclinic Bifurcation in Two Coupled Chua Oscillators

Dana

Roy

2007

Int. J. Bifurcation Chaos

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We report experimental observation of cycle-cycle bursting near homoclinic bifurcation in a self-oscillating Chua oscillator when it is diffusively coupled to another excitable Chua oscillator. The excitable oscillator induces an asymmetry in the self-oscillating Chua oscillator via coupling. The coupling strength controls the strength of the asymmetry that plays a key role in transition to bursting near homoclinic bifurcation.

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“…3 are strongly dependent on initial conditions. 47,48 It should be emphasized that we only considered the autonomous case of the Chua's circuit with a piecewise linear element. Other variants of the Chua's circuit with smooth nonlinearity and/or forcing functions, e.g., the MLC non-autonomous circuit 49 can have very rich varieties of dynamical phenomena and several ubiquitous routes to chaos such as quasiperiodicity, intermittency, period doubling, period-adding Farey sequence, and others.…”

Section: The Chua's Circuitmentioning

confidence: 99%

Controlling Chaos in a Chua's Circuit Using Notch Filters

Zaher

Abu-Rezq

2009

J CIRCUIT SYST COMP

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This paper explores the use of notch filters for the purpose of damping out chaotic oscillations. The design of the filter and the way it is interfaced to the system are investigated from a signal-processing point of view. A Chua's circuit, that has typical applications in synchronization and secure communications, is used to exemplify the suggested methodology where both theoretical and experimental results are provided. The power spectrum of the original system is analyzed to selectively damp-out portions of the power spectrum, thus truncating period-doubling, the original cause of chaos. Both single and double notch filters are explored to examine their effect on the performance of the modified system. Steady state analysis as well as issues regarding practical implementation are addressed and advantages and limitations of the proposed method are highlighted.

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Homoclinic bifurcation in Chua’s circuit

Cited by 30 publications

References 23 publications

Understanding the origin of extreme events in El Niño-Southern Oscillation

Understanding the origin of extreme events in El Niño-Southern Oscillation

Bursting Near Homoclinic Bifurcation in Two Coupled Chua Oscillators

Controlling Chaos in a Chua's Circuit Using Notch Filters

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