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20 pages, 819 KiB

Open AccessArticle

Lurie Control Systems Applied to the Sudden Cardiac Death Problem Based on Chua Circuit Dynamics

by Rafael F. Pinheiro, Diego Colón, Alexandre Antunes and Rui Fonseca-Pinto

Eng 2025, 6(5), 89; https://doi.org/10.3390/eng6050089 - 25 Apr 2025

Viewed by 388

Sudden cardiac death (SCD) represents a critical public health challenge, emphasizing the need for predictive techniques that model complex physiological dynamics. Studies indicate that the “V-trough” pattern in sympathetic nerve activity (SNA) could act as an early indicator of potentially fatal cardiac events, [...] Read more.

Sudden cardiac death (SCD) represents a critical public health challenge, emphasizing the need for predictive techniques that model complex physiological dynamics. Studies indicate that the “V-trough” pattern in sympathetic nerve activity (SNA) could act as an early indicator of potentially fatal cardiac events, which can be effectively modeled using a modified version of Chua’s chaotic system, incorporating the variables of heart rate (HR), SNA, and blood pressure (BP). This paper introduces a Chua circuit with delay, and proposes a novel control design technique based on Lurie-type control systems theory combined with mixed-sensitivity

H_{\infty}

(

S / K S / T

) methodology. The proposed controller enables precise regulation of HR in Chua’s circuit, both with and without delay, paving the way for the development of advanced devices capable of preventing SCD. Furthermore, the developed theory allows for the project of robust controllers for delayed Lurie systems within the single-input–single-output (SISO) framework. The presented theoretical framework, supported by numerical simulations, demonstrates the effectiveness of the conceptualization, marking a considerable advance in the understanding and early intervention of SCD through robust and nonlinear control systems. Full article

(This article belongs to the Section Electrical and Electronic Engineering)

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18 pages, 1176 KiB

Open AccessArticle

On Cauchy Problems of Caputo Fractional Differential Inclusion with an Application to Fractional Non-Smooth Systems

by Jimin Yu, Zeming Zhao and Yabin Shao

Mathematics 2023, 11(3), 653; https://doi.org/10.3390/math11030653 - 28 Jan 2023

Cited by 1 | Viewed by 1635

Abstract

In this innovative study, we investigate the properties of existence and uniqueness of solutions to initial value problem of Caputo fractional differential inclusion. In the study of existence problems, we considered the case of convex and non-convex multivalued maps. We obtained the existence [...] Read more.

In this innovative study, we investigate the properties of existence and uniqueness of solutions to initial value problem of Caputo fractional differential inclusion. In the study of existence problems, we considered the case of convex and non-convex multivalued maps. We obtained the existence results for both cases by means of the appropriate fixed point theorem. Furthermore, the uniqueness corresponding to both cases was also determined. Finally, we took a non-smooth system, the modified Murali–Lakshmanan–Chua (MLC) fractional-order circuit system, as an example to verify its existence and uniqueness conditions, and through several sets of simulation results, we discuss the implications. Full article

(This article belongs to the Special Issue Recent Investigations of Differential and Fractional Equations and Inclusions II)

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21 pages, 8596 KiB

Open AccessArticle

Slow–Fast Dynamics Behaviors under the Comprehensive Effect of Rest Spike Bistability and Timescale Difference in a Filippov Slow–Fast Modified Chua’s Circuit Model

by Shaolong Li, Weipeng Lv, Zhenyang Chen, Miao Xue and Qinsheng Bi

Mathematics 2022, 10(23), 4606; https://doi.org/10.3390/math10234606 - 5 Dec 2022

Cited by 1 | Viewed by 2135

Abstract

Since the famous slow–fast dynamical system referred to as the Hodgkin–Huxley model was proposed to describe the threshold behaviors of neuronal axons, the study of various slow–fast dynamical behaviors and their generation mechanisms has remained a popular topic in modern nonlinear science. The [...] Read more.

Since the famous slow–fast dynamical system referred to as the Hodgkin–Huxley model was proposed to describe the threshold behaviors of neuronal axons, the study of various slow–fast dynamical behaviors and their generation mechanisms has remained a popular topic in modern nonlinear science. The primary purpose of this paper is to introduce a novel transition route induced by the comprehensive effect of special rest spike bistability and timescale difference rather than a common bifurcation via a modified Chua’s circuit model with an external low-frequency excitation. In this paper, we attempt to explain the dynamical mechanism behind this novel transition route through quantitative calculations and qualitative analyses of the nonsmooth dynamics on the discontinuity boundary. Our work shows that the whole system responses may tend to be various and complicated when this transition route is triggered, exhibiting rich slow–fast dynamics behaviors even with a very slight change in excitation frequency, which is described well by using Poincaré maps in numerical simulations. Full article

(This article belongs to the Special Issue Modeling and Analysis in Dynamical Systems and Bistability)

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16 pages, 7235 KiB

Open AccessArticle

Non-Smooth Dynamic Behaviors as well as the Generation Mechanisms in a Modified Filippov-Type Chua’s Circuit with a Low-Frequency External Excitation

by Hongfang Han, Shaolong Li and Qinsheng Bi

Mathematics 2022, 10(19), 3613; https://doi.org/10.3390/math10193613 - 2 Oct 2022

Cited by 2 | Viewed by 1896

Abstract

The main purpose of this paper is to study point-cycle type bistability as well as induced periodic bursting oscillations by taking a modified Filippov-type Chua’s circuit system with a low-frequency external excitation as an example. Two different kinds of bistable structures in the [...] Read more.

The main purpose of this paper is to study point-cycle type bistability as well as induced periodic bursting oscillations by taking a modified Filippov-type Chua’s circuit system with a low-frequency external excitation as an example. Two different kinds of bistable structures in the fast subsystem are obtained via conventional bifurcation analyses; meanwhile, nonconventional bifurcations are also employed to explain the nonsmooth structures in the bistability. In the following numerical investigations, dynamic evolutions of the full system are presented by regarding the excitation amplitude and frequency as analysis parameters. As a consequence, we can find that the classification method for periodic bursting oscillations in smooth systems is not completely applicable when nonconventional bifurcations such as the sliding bifurcations and persistence bifurcation are involved; in addition, it should be pointed out that the emergence of the bursting oscillation does not completely depend on bifurcations under the point-cycle bistable structure in this paper. It is predicted that there may be other unrevealed slow–fast transition mechanisms worthy of further study. Full article

(This article belongs to the Special Issue Modeling and Analysis in Dynamical Systems and Bistability)

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23 pages, 7250 KiB

Open AccessArticle

FPGA-Based Antipodal Chaotic Shift Keying Communication System

by Filips Capligins, Anna Litvinenko, Deniss Kolosovs, Maris Terauds, Maris Zeltins and Dmitrijs Pikulins

Electronics 2022, 11(12), 1870; https://doi.org/10.3390/electronics11121870 - 14 Jun 2022

Cited by 12 | Viewed by 2766

Abstract

The current work presents a novel digital chaotic communication system with antipodal chaotic shift keying modulation, implemented in a field-programmable gate array (FPGA). Such systems provide high security on the physical communication level and can be used in wireless sensor network systems. A [...] Read more.

The current work presents a novel digital chaotic communication system with antipodal chaotic shift keying modulation, implemented in a field-programmable gate array (FPGA). Such systems provide high security on the physical communication level and can be used in wireless sensor network systems. A modified Chua circuit chaos generator and error linear feedback chaotic synchronization are implemented in FPGA and used to develop a chaotic communication system with digital transmitter and receiver an analog in-between signal transmission. Additionally, a validated mathematical model of the communication system prototype is created in the Simulink environment, which is used to compare the performance of the prototype and its nodes with the simulation and simplify its development. The performance is evaluated using simulation with the additive white Gaussian noise channel and analyzing the bit error ratio. Full article

(This article belongs to the Special Issue Design and Applications of Nonlinear Circuits and Systems)

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17 pages, 5903 KiB

Open AccessArticle

Complex Oscillations of Chua Corsage Memristor with Two Symmetrical Locally Active Domains

by Jiajie Ying, Yan Liang, Fupeng Li, Guangyi Wang and Yiran Shen

Electronics 2022, 11(4), 665; https://doi.org/10.3390/electronics11040665 - 21 Feb 2022

Cited by 5 | Viewed by 2392

Abstract

This paper proposes a modified Chua Corsage Memristor endowed with two symmetrical locally active domains. Under the DC bias voltage in the locally active domains, the memristor with an inductor can construct a second-order circuit to generate periodic oscillation. Based on the theories [...] Read more.

This paper proposes a modified Chua Corsage Memristor endowed with two symmetrical locally active domains. Under the DC bias voltage in the locally active domains, the memristor with an inductor can construct a second-order circuit to generate periodic oscillation. Based on the theories of the edge of chaos and local activity, the oscillation mechanism of the symmetrical periodic oscillations of the circuit is revealed. The third-order memristor circuit is constructed by adding a passive capacitor in parallel with the memristor in the second-order circuit, where symmetrical periodic oscillations and symmetrical chaos emerge either on or near the edge of chaos domains. The oscillation mechanisms of the memristor-based circuits are analyzed via Domains distribution maps, which include the division of locally passive domains, locally active domains, and the edge of chaos domains. Finally, the symmetrical dynamic characteristics are investigated via theory and simulations, including Lyapunov exponents, bifurcation diagrams, and dynamic maps. Full article

(This article belongs to the Special Issue Memristive Devices and Systems: Modelling, Properties & Applications)

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13 pages, 5244 KiB

Open AccessArticle

Fractional-Order Analysis of Modified Chua’s Circuit System with the Smooth Degree of 3 and Its Microcontroller-Based Implementation with Analog Circuit Design

by Junxia Wang, Li Xiao, Karthikeyan Rajagopal, Akif Akgul, Serdar Cicek and Burak Aricioglu

Symmetry 2021, 13(2), 340; https://doi.org/10.3390/sym13020340 - 19 Feb 2021

Cited by 20 | Viewed by 3606

Abstract

In the paper, we futher consider a fractional-order system from a modified Chua’s circuit system with the smooth degree of 3 proposed by Fu et al. Bifurcation analysis, multistability and coexisting attractors in the the fractional-order modified Chua’s circuit are studied. In addition, [...] Read more.

In the paper, we futher consider a fractional-order system from a modified Chua’s circuit system with the smooth degree of 3 proposed by Fu et al. Bifurcation analysis, multistability and coexisting attractors in the the fractional-order modified Chua’s circuit are studied. In addition, microcontroller-based circuit was implemented in real digital engineering applications by using the fractional-order Chua’s circuit with the piecewise-smooth continuous system. Full article

(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits Ⅱ)

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16 pages, 1518 KiB

Open AccessArticle

Three-Saddle-Foci Chaotic Behavior of a Modified Jerk Circuit with Chua’s Diode

by Pattrawut Chansangiam

Symmetry 2020, 12(11), 1803; https://doi.org/10.3390/sym12111803 - 30 Oct 2020

Cited by 4 | Viewed by 2526

Abstract

This paper investigates the chaotic behavior of a modified jerk circuit with Chua’s diode. The Chua’s diode considered here is a nonlinear resistor having a symmetric piecewise linear voltage-current characteristic. To describe the system, we apply fundamental laws in electrical circuit theory to [...] Read more.

This paper investigates the chaotic behavior of a modified jerk circuit with Chua’s diode. The Chua’s diode considered here is a nonlinear resistor having a symmetric piecewise linear voltage-current characteristic. To describe the system, we apply fundamental laws in electrical circuit theory to formulate a mathematical model in terms of a third-order (jerk) nonlinear differential equation, or equivalently, a system of three first-order differential equations. The analysis shows that this system has three collinear equilibrium points. The time waveform and the trajectories about each equilibrium point depend on its associated eigenvalues. We prove that all three equilibrium points are of type saddle focus, meaning that the trajectory of

(x (t), y (t))

diverges in a spiral form but

z (t)

converges to the equilibrium point for any initial point

(x (0), y (0), z (0))

. Numerical simulation illustrates that the oscillations are dense, have no period, are highly sensitive to initial conditions, and have a chaotic hidden attractor. Full article

(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits)

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