Lienard chaotic system based on Duffing and the Sinc function for weak signals detection

Pancoatl-Bortolotti, Pedro; Enríquez-Caldera, Rogerio A.; Costa, A.H.; Guerrero-Castellanos, J.F.; Tello-Bello, Maribel

doi:10.1109/tla.2022.9853234

Cited by 7 publications

(6 citation statements)

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“…Previous work has demonstrated that the use of weakly chaotic nonlinear oscillators increases the probability of achieving high signal detection rates compared to strongly chaotic ones. 19,29 F I G U R E 2 Dynamics of the VTD Liènard oscillator configured in chaotic intermittence.…”

Section: Non-liènard System In Chaos-periodicity Intermittencementioning

confidence: 99%

“…To ensure the intermittence regime in the VTD oscillator, the parameter values are tuned according to the search iterative procedure described in reference 19. The critical state is found using the Lyapunov exponent (

λ

) obtained from Equation 1 and following the next criteria: when

λ > 0

corresponds to a chaotic behavior and when

λ < 0

to a periodic behavior.…”

Section: Design Of the Non‐liènard Oscillatormentioning

confidence: 99%

“…When we force our potential function as

V = \frac{1}{2} x^{2} + \frac{1}{4} x^{4} + 0.51 x \cos ωt

, 27,28 it produces a double‐well potential, which corresponds in the phase space to various energy curves, including homoclinic orbits, as shown in Figure 3B, promoting quasi‐chaotic oscillations. Previous work has demonstrated that the use of weakly chaotic nonlinear oscillators increases the probability of achieving high signal detection rates compared to strongly chaotic ones 19,29 …”

Section: Design Of the Non‐liènard Oscillatormentioning

confidence: 99%

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Adaptive Doppler bio‐signal detector and time‐frequency representation based on non‐Liènard oscillator

Pancóatl‐Bortolotti,

Enríquez‐Caldera,

Costa

et al. 2023

Numer Methods Biomed Eng

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The work presented here provides the guidelines and results for designing and implementing a highly sensitive modified Van der Pol – Duffing oscillator with a trigonometric damping function (VTD). This VTD can exhibit periodic and quasi‐chaotic behavior necessary for application in weak signal detection. Here, we present two proposals: (1) A method based on a quasi‐chaotic intermittent array (ANLIOA), whose all VTD parameters are calculated and fine‐tuned toward a critical state between chaotic and periodic state through a Lyapunov exponent procedure, and (2) A method based on a single oscillator in an adaptive stopping oscillation system (ANLSOS), where VTD is established within an oscillatory regime. Both systems can detect non‐stationary signals while reconstructing the time‐frequency spectrogram in high resolution within severe noise conditions. The systems were adapted for the detection of a synthesized Doppler signal corresponding to the blood flow velocity profile from an artery. Comparative results using typical oscillators such as Duffing or Van der Pol demonstrate the superiority of the VTD oscillator in detection when used for both methods, whose mean absolute percentage error reached around 6% for a signal‐to‐noise ratio (SNR) of −10 dB. Furthermore, compared to other time‐frequency methods, ANLIOA and ANLSOS promise high precision in detecting Doppler signals with low rates of frequency changes while minimizing energy emission and avoiding possible bio‐thermal effects.

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Section: Non-liènard System In Chaos-periodicity Intermittencementioning

confidence: 99%

λ

) obtained from Equation 1 and following the next criteria: when

λ > 0

corresponds to a chaotic behavior and when

λ < 0

to a periodic behavior.…”

Section: Design Of the Non‐liènard Oscillatormentioning

confidence: 99%

“…When we force our potential function as

V = \frac{1}{2} x^{2} + \frac{1}{4} x^{4} + 0.51 x \cos ωt

Section: Design Of the Non‐liènard Oscillatormentioning

confidence: 99%

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Adaptive Doppler bio‐signal detector and time‐frequency representation based on non‐Liènard oscillator

Pancóatl‐Bortolotti,

Enríquez‐Caldera,

Costa

et al. 2023

Numer Methods Biomed Eng

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“…whose parameters ε, αβ, must be positive to accomplish the theorem conditions [17]- [19]. This Liènard system is modeled with the state equations…”

Section: A Limit Cycle In the Type-liènard Systemmentioning

confidence: 99%

“…Once the self-oscillation conditions are satisfied for the proposed system, there is the need to assure the presence of chaotic oscillations by properly selecting its parameters that enable the system to work into a chaos-periodicity intermittence regime. For this purpose, let us generically name µ each at the time all parameters involved in Eq.3 and use both: first, the method described in [20] for time series where the maximum LE λ(µ) is calculated as a function of the single system parameter under exploration and second, the method using the Melnikov function M (µ) as it is described in Algorithm 1 of [19] to properly establish the specific and suitable value for every single µ.…”

Section: B Intermittent Statementioning

confidence: 99%

Time-Frequency High Resolution Using Chaos In Detection

Pancoatl-Bortolotti¹,

Enríquez-Caldera²,

Costa³

et al. 2022

Preprint

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<p>A non-linear Liènard-type system based on trigono-metric functions is designed and used as a highly sensitive signal detector. Based on the intermittence mechanism presented in some chaotic systems, an adaptive detection array formed by five chaotic oscillators is designed, tuned, and tested. In the array, each individual oscillator identifies changes in frequency for non-stationary weak signals and, with the array working in an adaptative mode, gives an estimate of the timing at which intermittence occurred allowing the representation of a time-frequency spectrogram even when high-level noise is present. This work also shows that the trigonometric based system has an asymptotically stable limit cycle centered at the origin through two methods: first under the fixed-point analysis and later by the Melnikov method that uses a family of periodic orbits. Once the self-sustained oscillations are produced, the system is configured to drive itself into a saddle-node bifurcation through an iterative method for searching and tuning parameters which, in turn, assures the route to chaotic intermittence. Through this mechanism, the new system can be used as a non-stationary signal detector that also provides a high resolution time-frequency representation. The computer experiments showed that the adaptive array is perfectly compatible with other second-order non-linear oscillators configured in the chaotic intermittence regime such as Duffing, Van der Pol, and Van der Pol - Duffing, achieving high detection rates under noisy conditions. Moreover, when the new Liènard-type oscillators are incorporated into the adaptive array, the detection sensitivity overcomes the SNR threshold present in all oscillators mentioned above and allows for reaching and maintaining a relative error around 1% under severe noise conditions down to about -60 dB SNR.</p>

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Study on fractional-order coupling of high-order Duffing oscillator and its application

Li,

Xie,

Yang

2024

Chaos, Solitons & Fractals

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Lienard chaotic system based on Duffing and the Sinc function for weak signals detection

Cited by 7 publications

References 0 publications

Adaptive Doppler bio‐signal detector and time‐frequency representation based on non‐Liènard oscillator

Adaptive Doppler bio‐signal detector and time‐frequency representation based on non‐Liènard oscillator

Time-Frequency High Resolution Using Chaos In Detection

Study on fractional-order coupling of high-order Duffing oscillator and its application

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