Antimonotonicity, chaos, quasi-periodicity and coexistence of hidden attractors in a new simple 4-D chaotic system with hyperbolic cosine nonlinearity

Signing, V. R. Folifack; Kengne, Jacques; Pone, Justin Roger Mboupda

doi:10.1016/j.chaos.2018.10.018

Cited by 37 publications

(16 citation statements)

References 56 publications

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“…Besides, the phenomenon antimonotonicity is stated in Figure 7a, which refers to the creation of period orbits followed by their nullification with reverse bifurcation sequences [77]. This phenomenon is one of the most common paths to chaos [78,79]. Antimonotonicity was found in Equation ( 5) by sweeping a 7 in the interval 2.6 ≤ a 7 ≤ 3.2 with q = 0.95.…”

Section: Hypoglycemia: Parameter a 1 As A Function Of Fractional-order Qmentioning

confidence: 99%

The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

2020

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For studying biological conditions with higher precision, the memory characteristics defined by the fractional-order versions of living dynamical systems have been pointed out as a meaningful approach. Therefore, we analyze the dynamics of a glucose-insulin regulatory system by applying a non-local fractional operator in order to represent the memory of the underlying system, and whose state-variables define the population densities of insulin, glucose, and β-cells, respectively. We focus mainly on four parameters that are associated with different disorders (type 1 and type 2 diabetes mellitus, hypoglycemia, and hyperinsulinemia) to determine their observation ranges as a relation to the fractional-order. Like many preceding works in biosystems, the resulting analysis showed chaotic behaviors related to the fractional-order and system parameters. Subsequently, we propose an active control scheme for forcing the chaotic regime (an illness) to follow a periodic oscillatory state, i.e., a disorder-free equilibrium. Finally, we also present the electronic realization of the fractional glucose-insulin regulatory model to prove the conceptual findings.

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Section: Hypoglycemia: Parameter a 1 As A Function Of Fractional-order Qmentioning

confidence: 99%

The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

2020

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“…= −J(X(t)) ∈ R m×m is the conservative matrix and G(X(t)) ∈ R m×o , which is selected as an identity matrix of appropriate dimension. The matrix J(X(t)) is given as [31] J(X(t)) = 0 I −I 0 (14) with identity and zero matrices of appropriate dimension. The Hamiltonian and Lagrangian are given by [31]…”

Section: Problem Formulationmentioning

confidence: 99%

“…In the literature there are many studies in which hidden attractors are analyzed, for example, in [13], a new 3-D chaotic system with hidden attractor is designed and analyzed in which the eigenvalues and Lyapunov exponents are obtained for dynamical analysis purposes. Other examples can be found in [14], in which a simple 4-D chaotic system is evinced in the presence of a hyperbolic cosine nonlinearity, where some phenomenons such as multistability, antimonotonicity, and quasi-periodic orbits are analyzed. In [15], the multistability phenomenon is related to the occurrence of unpredictable attractors which are called hidden attractor.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of Port Hamiltonian Chaotic Systems with Hidden Attractors by Adaptive Terminal Sliding Mode Control

Azar

Serrano

2020

Entropy

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In this study, the design of an adaptive terminal sliding mode controller for the stabilization of port Hamiltonian chaotic systems with hidden attractors is proposed. This study begins with the design methodology of a chaotic oscillator with a hidden attractor implementing the topological framework for its respective design. With this technique it is possible to design a 2-D chaotic oscillator, which is then converted into port-Hamiltonia to track and analyze these models for the stabilization of the hidden chaotic attractors created by this analysis. Adaptive terminal sliding mode controllers (ATSMC) are built when a Hamiltonian system has a chaotic behavior and a hidden attractor is detected. A Lyapunov approach is used to formulate the adaptive device controller by creating a control law and the adaptive law, which are used online to make the system states stable while at the same time suppressing its chaotic behavior. The empirical tests obtaining the discussion and conclusions of this thesis should verify the theoretical findings.

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“…From then on, memristor has been become a research focus in the area of circuit and computer [1]- [4], two main branches of which are physical design and mathematical modeling. Interestingly even hyperbolic sine function [5]- [7], hyperbolic cosine function [8], [9], or even hyperbolic tangent function [10], [11] is used to model memristor for chaos producing.…”

Section: Introductionmentioning

confidence: 99%

A Conditional Symmetric Memristive System With Infinitely Many Chaotic Attractors

Chen

et al. 2020

IEEE Access

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A chaotic system with a hyperbolic function flux-controlled memristor is designed, which exhibits conditional symmetry and attractor growing. The newly introduced cosine function keeps the polarity balance when some of the variables get polarity inversed and correspondingly conditional symmetric coexisting chaotic attractors are coined. Due to the periodicity of the cosine function, the memristive system with infinitely many coexisting attractors shows attractor growing in some special circumstances. Analog circuit experiment proves the theoretical and numerical analysis.

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Antimonotonicity, chaos, quasi-periodicity and coexistence of hidden attractors in a new simple 4-D chaotic system with hyperbolic cosine nonlinearity

Cited by 37 publications

References 56 publications

The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

The Effect of a Non-Local Fractional Operator in an Asymmetrical Glucose-Insulin Regulatory System: Analysis, Synchronization and Electronic Implementation

Stabilization of Port Hamiltonian Chaotic Systems with Hidden Attractors by Adaptive Terminal Sliding Mode Control

A Conditional Symmetric Memristive System With Infinitely Many Chaotic Attractors

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