Lyapunov Exponents for Dynamic Equations on Time Scales

Nguyen, Khong Chi; Nhung, Tran Van; Hoa, T.T. Anh; Liem, Nguyen Chi

doi:10.12732/dsa.v27i2.10

Cited by 5 publications

(4 citation statements)

References 9 publications

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“…For generic syndetic time scales, a similar estimate was established in [14], see the following statement. Let…”

Section: Hilger Functions and Lyapunov Exponentssupporting

confidence: 55%

“…For time scales, instead of using one of the logarithm functions, mentioned above, we can use the following definition [14]. Even though the Lyapunov exponents depend significantly on the selection of a time scale, the following statement is true.…”

Section: Hilger Functions and Lyapunov Exponentsmentioning

confidence: 99%

“…+ α n . The existence of a normal fundamental matrix is proved in [14], and the proof of that statement is similar to the case of ordinary differential equations [1].…”

Section: Hilger Functions and Lyapunov Exponentsmentioning

confidence: 99%

See 2 more Smart Citations

Linear Impulsive Dynamic Systems

Georgiev

2019

Functional Dynamic Equations on Time Scales

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We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For ∆-differential operators, corresponding to linear dynamic systems we consider their solvability in various functional spaces. Based on these techniques, we prove several results on the existence of a bounded solution for some systems with small nonlinearities. Thus we introduce some generalizations of the classic hyperbolicity property (exponential dichotomy) for systems of ordinary differential equations.Besides, we introduce the Lyapunov regularity condition that coincides with the classic one for ordinary differential equations. For regular systems, we prove some criteria for the existence of bounded solutions of perturbed systems.

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“…For generic syndetic time scales, a similar estimate was established in [14], see the following statement. Let…”

Section: Hilger Functions and Lyapunov Exponentssupporting

confidence: 55%

Section: Hilger Functions and Lyapunov Exponentsmentioning

confidence: 99%

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Linear Impulsive Dynamic Systems

Georgiev

2019

Functional Dynamic Equations on Time Scales

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“…In phase space, Lyapunov Exponents (LE) can be used to discriminate the output state of system qualitatively [16], which denotes the average exponential rates of divergence or convergence of error |δr| between two adjacent points on the orbit through time t.…”

Section: B Chaotic Systemmentioning

confidence: 99%

Chaos Detection Scheme for Multiple Variable Frequency Signals with Overlapping Frequencies

Chen

Shi

2023

Preprint

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As one of the most critical technology in signal detection, weak signal detection (WSD) has received a great deal of attention in many areas. Traditional methods perform well when the number of signal is single and the form of signal is simple, which are quite different from the situation in some real applications (e.g., the marine communication scenario). In this paper, we consider the problem of high-precision frequency detection of Multiple Variable-Frequency Signals with Overlapping frequencies (MVFS-O) in the low signal-to-noise ratio (SNR) scenario, whose key point is how to detect the parameters (frequency range and frequency modulation rate (FMR)) of each signal. To solve the problem, a novel chaos detection scheme based on Duffing difference oscillator is proposed. In this scheme, the wide frequency detection range of the critical state is used to determine the frequency range of the signals quickly, and the Lyapunov Exponent is used to discriminate the output state of the system qualitatively. Furthermore, combining with the time points of the periodic state of the system, we can obtain the FMR of the corresponding signal by analyzing overlapping frequency ratio. Numerical results are provided to verify the practical effectiveness of the proposed scheme.

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Weak Signal Detection Based on Improved Double-Coupled System and Section Variance Method

Jiang

Zhao

et al. 2022

2022 IEEE 8th International Conference on Computer and Communications (ICCC)

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Lyapunov Exponents for Dynamic Equations on Time Scales

Cited by 5 publications

References 9 publications

Linear Impulsive Dynamic Systems

Linear Impulsive Dynamic Systems

Chaos Detection Scheme for Multiple Variable Frequency Signals with Overlapping Frequencies

Weak Signal Detection Based on Improved Double-Coupled System and Section Variance Method

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