Generating Shilnikov chaos in 3D piecewise linear systems

Barajas-Ramírez, Juan Gonzalo; Franco-López, Arturo; González-Hernández, Hugo G.

doi:10.1016/j.amc.2020.125877

Cited by 10 publications

(3 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This paper includes two classifications of heteroclinic cycles: regular and singular, as well as degenerated and nondegenerated. Other findings can be found in papers such as that in [ 66 ], which demonstrates a design methodology and algorithm for implementing geometric features with focus-saddle and center node equilibrium points.…”

Section: Related Workmentioning

confidence: 81%

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Azar

Serrano

Zhu

et al. 2021

Entropy

View full text Add to dashboard Cite

In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.

show abstract

Section: Related Workmentioning

confidence: 81%

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Azar

Serrano

Zhu

et al. 2021

Entropy

View full text Add to dashboard Cite

show abstract

“…The above approximation for the Jacobian of the local dynamics has been previously validated for saddle-focus oscillators (e.g., the Rössler system) in [22]. Based on the definition of a hyperbolic saddle-focus equilibrium point in [23], we see that the Chua circuit can also be considered a saddle-focus oscillator, so the analysis presented in [22] applies to that case too, as well as to the case of Bernoulli maps [11]. While this particular assumption results in a loss of generality, it allows us to extend the theory to the case of large parameter mismatches and to analyze whether parameter mismatches either enhance or hinder synchronization, a question that did not find an answer in [10].…”

Section: Examplementioning

confidence: 99%

Synchronization in networks of coupled oscillators with mismatches

Nazerian

Panahi

Sorrentino

2023

EPL

View full text Add to dashboard Cite

This perspective reviews the subject of synchronization in networks of coupled non-phase oscillators in the presence of parametric mismatches. We first discuss the case of small parametric mismatches, for which the conditions for stability of the synchronous solution are the same as in the case of identical oscillators, but the synchronization error increases with the size of the mismatches. We then analyze the case of larger parameter mismatches and provide an explanation for why parameter mismatches sometimes hinder and sometimes enhance stability of the synchronous solution.

show abstract

“…In recent years, Belykh et al [4,5] confirmed that a piecewise linear system has sliding homoclinic orbits and heteroclinic cycles, and discussed the complex dynamics similar to the Lorenz system by rigorously analyzing the constructed return map. Barajas et al [2] calculated a homoclinic orbit for a piecewise linear system, where a technique developed is by taking the geometric feature of the manifolds. Lu and Yang [27] rigorously demonstrated existence of an isolated heteroclinic cycle and chaotic sets in a class of PWASs with two discontinuous boundaries, which consists of three sub-systems: the middle one has three real roots, the others both have two different types of eigenvalues including a pair of conjugate complex roots and a real root, and three real roots.…”

mentioning

confidence: 99%

Coexisting singular cycles in a class of three-dimensional three-zone piecewise affine systems

2022

DCDS-B

View full text Add to dashboard Cite

<p style='text-indent:20px;'>Detecting an isolated homoclinic or heteroclinic cycle is a great challenge in a concrete system, letting alone the case of coexisting scenarios and more complicated chaotic behaviors. This paper systematically investigates the dynamics for a class of three-dimensional (3D) three-zone piecewise affine systems (PWASs) consisting of three sub-systems. Interestingly, under different conditions the considered system can display three types of coexisting singular cycles including: homoclinic and homoclinic cycles, heteroclinic and heteroclinic cycles, homoclinic and heteroclinic cycles. Furthermore, it establishes sufficient conditions for the presence of chaotic invariant sets emerged from such coexisting cycles. Finally, three numerical examples are provided to verify the proposed theoretical results.</p>

show abstract

Generating Shilnikov chaos in 3D piecewise linear systems

Cited by 10 publications

References 29 publications

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Synchronization in networks of coupled oscillators with mismatches

Coexisting singular cycles in a class of three-dimensional three-zone piecewise affine systems

Contact Info

Product

Resources

About