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1
Content available Bifurcation analysis, circuit design and sliding mode control of a new multistable chaotic population model with one prey and two predators
Vaidyanathan Sundarapandian, Benkouider Khaled, Sambas Aceng, Darwin P.
Archives of Control Sciences
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2023
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Vol. 33, No. 1
127--153
EN
In this work, we report a new chaotic population biology system with one prey and two predators. Our new chaotic population model is derived by introducing two nonlinear interaction terms between the prey and predator-2 to the Samardzija-Greller population biology system (1988). We show that the new chaotic population biology system has a greater value of Maximal Lyapunov Exponent (MLE) than the Maximal Lyapunov Exponent (MLE) of the Samardzija-Greller population biology system (1988). We carry out a detailed bifurcation analysis of the new chaotic population biology system with one prey and two predators. We also show that the new chaotic population biology model exhibits multistability with coexisting chaotic attractors. Next, we use the integral sliding mode control (ISMC) for the complete synchronization of the new chaotic population biology system with itself, taken as the master and slave chaotic population biology systems. Finally, for practical use of the new chaotic population biology system, we design an electronic circuit design using Multisim (Version 14.0).
2
Content available A new modified WINDMI jerk system with exponential and sinusoidal nonlinearities, its bifurcation analysis, multistability, circuit simulation and synchronization design
Mohamed Mohamad Afendee, Vaidyanathan Sundarapandian, Hannachi Fareh, Sambas Aceng, Darwin P.
Archives of Control Sciences
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2023
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Vol. 33, No. 4
711--735
EN
In this work, a new 3-D modified WINDMI chaotic jerk system with exponential and sinusoidal nonlinearities is presented and its dynamical behaviours and properties are investigated. Firstly, some properties of the system are studied such as equilibrium points and their stability, Lyapunov exponents and Kaplan-Yorke dimension. Also, we study the new jerk system dynamics using numerical simulations and analyses, including phase portraits, Lyapunouv exponent spectrum, bifurcation diagram and Poincaré map, 0-1 test. Next, we exhibit that the new 3-D chaotic modified WINDMI jerk system has multistability with coexisting chaotic attractors. Moreover, we design an electronic circuit using MultiSim 14.1 for real implementation of the modified WINDMI chaotic jerk system. Finally, we design an active synchronization scheme for the complete synchronization of the modified WINDMI chaotic jerk systems via backstepping control.
3
Content available Hybrid synchronization and parameter estimation of a complex chaotic network of permanent magnet synchronous motors using adaptive integral sliding mode control
Siddique Nazam, Rehman Fazal U.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2021
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Vol. 69, nr 3
art. no. e137056
EN
The synchronisation of a complex chaotic network of permanent magnet synchronous motor systems has increasing practical importance in the field of electrical engineering. This article presents the control design method for the hybrid synchronization and parameter estimation of ring-connected complex chaotic network of permanent magnet synchronous motor systems. The design of the desired control law is a challenging task for control engineers due to parametric uncertainties and chaotic responses to some specific parameter values. Controllers are designed based on the adaptive integral sliding mode control to ensure hybrid synchronization and estimation of uncertain terms. To apply the adaptive ISMC, firstly the error system is converted to a unique system consisting of a nominal part along with the unknown terms which are computed adaptively. The stabilizing controller incorporating nominal control and compensator control is designed for the error system. The compensator controller, as well as the adopted laws, are designed to get the first derivative of the Lyapunov equation strictly negative. To give an illustration, the proposed technique is applied to 4-coupled motor systems yielding the convergence of error dynamics to zero, estimation of uncertain parameters, and hybrid synchronization of system states. The usefulness of the proposed method has also been tested through computer simulations and found to be valid.
4
Content available A new 4-D hyperchaotic system with no equilibrium, its multistability, offset boosting and circuit simulation
Vaidyanathan Sundarapandian, Moroz Irene M., Sambas Aceng
Archives of Control Sciences
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2020
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Vol. 30, No. 3
575--597
EN
A new 4-D dynamical system with hyperchaos is reported in this work. It is shown that the proposed nonlinear dynamical system with hyperchaos has no equilibrium point. Hence, the new dynamical system exhibits hidden hyperchaotic attractor. An in-depth dynamic analysis of the new hyperchaotic system is carried out with bifurcation transition diagrams, multistability analysis, period-doubling bubbles and offset boosting analysis. Using Integral Sliding Mode Control (ISMC), global hyperchaos synchronization results of the new hyperchaotic system are described in detail. Furthermore, an electronic circuit realization of the new hyperchaotic system has been simulated in MultiSim software version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB.
5
Content available Chaos in a simple snap system with only one nonlinearity, its adaptive control and real circuit design
Pham Viet-Thanh, Vaidyanathan Sundarapandian, Volos Christos, Jafari Sajad, Alsaadi Fawaz E., Alsaadi Fuad E.
Archives of Control Sciences
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2019
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Vol. 29, No. 1
73--96
EN
We study an elegant snap system with only one nonlinear term, which is a quadratic nonlinearity. The snap system displays chaotic attractors, which are controlled easily by changing a system parameter. By using analysis, simulations and a real circuit, the dynamics of such a snap system has been investigated. We also investigate backstepping based adaptive control schemes for the new snap system with unknown parameters.
6
Content available A new 4-D dynamical system exhibiting chaos with a line of rest points, its synchronizationand circuit model
Vaidyanathan Sundarapandian, Sambas Aceng, Zhang Sen
Archives of Control Sciences
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2019
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Vol. 29, No. 3
485--506
EN
A new 4-D dynamical system exhibiting chaos is introduced in this work. The proposed nonlinear plant with chaos has an unstable rest point and a line of rest points. Thus, the new nonlinear plant exhibits hidden attractors. A detailed dynamic analysis of the new nonlinear plant using bifurcation diagrams is described. Synchronization result of the new nonlinear plant with itself is achieved using Integral Sliding Mode Control (ISMC). Finally, a circuit modelusing MultiSim of the new 4-D nonlinear plant with chaos is carried out for practical use.
7
Content available A new chaotic system with axe-shaped equilibrium, its circuit implementation and adaptive synchronization
Vaidyanathan S., Sambas A., Mamat M.
Archives of Control Sciences
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2018
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Vol. 28, No. 3
443--462
EN
In the recent years, chaotic systems with uncountable equilibrium points such as chaotic systems with line equilibrium and curve equilibrium have been studied well in the literature. This reports a new 3-D chaotic system with an axe-shaped curve of equilibrium points. Dynamics of the chaotic system with the axe-shaped equilibrium has been studied by using phase plots, bifurcation diagram, Lyapunov exponents and Lyapunov dimension. Furthermore, an electronic circuit implementation of the new chaotic system with axe-shaped equilibrium has been designed to check its feasibility. As a control application, we report results for the synchronization of the new system possessing an axe-shaped curve of equilibrium points.
8
Content available A 4-D chaotic hyperjerk system with a hidden attractor, adaptive backstepping control and circuit design
Vaidyanathan S., Jafari S., Pham V.-T., Azar A. T., Alsaadi F. E.
Archives of Control Sciences
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2018
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Vol. 28, No. 2
239--254
EN
A novel 4-D chaotic hyperjerk system with four quadratic nonlinearities is presented in this work. It is interesting that the hyperjerk system has no equilibrium. A chaotic attractor is said to be a hidden attractor when its basin of attraction has no intersection with small neighborhoods of equilibrium points of the system. Thus, our new non-equilibrium hyperjerk system possesses a hidden attractor. Chaos in the system has been observed in phase portraits and verified by positive Lyapunov exponents. Adaptive backstepping controller is designed for the global chaos control of the non-equilibrium hyperjerk system with a hidden attractor. An electronic circuit for realizing the non-equilibrium hyperjerk system is also introduced, which validates the theoretical chaotic model of the hyperjerk system with a hidden chaotic attractor.
9
Content available A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot
Vaidyanathan S., Sambas A., Mamat M., Sanjaya M.
Archives of Control Sciences
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2017
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Vol. 27, no. 4
541--554
EN
This research work proposes a new three-dimensional chaotic system with a hidden attractor. The proposed chaotic system consists of only two quadratic nonlinearities and the system possesses no critical points. The phase portraits and basic qualitative properties of the new chaotic system such as Lyapunov exponents and Lyapunov dimension have been described in detail. Finally, we give some engineering applications of the new chaotic system like circuit simulation and control of wireless mobile robot.
10
Content available A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control
Vaidyanathan S.
Archives of Control Sciences
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2017
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Vol. 27, no. 3
409--439
EN
This paper presents a new seven-term 3-D jerk chaotic system with two cubic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0:2974, L2 = 0 and L3 = −3:8974. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the new jerk chaotic system is found as DKY = 2:0763. Next, an adaptive backstepping controller is designed to globally stabilize the new jerk chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations are shown to illustrate all the main results derived in this work.
11
Content available remote Modelowanie dynamiki chaotycznej w środowisku Matlab-Simulink
Modzelewski P., Citko W.
Zeszyty Naukowe Akademii Morskiej w Gdyni
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2011
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nr 70
45-61
PL
Systemy dynamiczne opisane nieliniowymi równaniami różniczkowymi stanowią efektywny model wielu zjawisk fizycznych. Bardzo interesującą klasę tych systemów tworzą układy generujące deterministyczne drgania chaotyczne. W tym artykule przedstawiono opracowane w środowisku Matlab-Simulink modele wybranych układów chaotycznych. Zaprezentowano także wyniki symulacji uzyskane dla różnych wartości parametrów kontrolnych. Otrzymane rezultaty potwierdzają skuteczność środowiska Matlab w modelowaniu układów chaotycznych.
EN
Nonlinear dynamic systems described by differential equations are an effective model for many physical phenomena. Systems that generate deterministic chaotic oscillations create very interesting class of dynamical systems. In this article, models of selected chaotic systems developed in Matlab- -Simulink environment are presented. As well the simulation results obtained for different values of control parameters are presented. The results confirm the effectiveness of the Matlab modeling of chaotic systems.
12
Content available remote On fractal dimension estimation
Pánek D., Kropik P., Predota A.
Przegląd Elektrotechniczny
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2011
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R. 87, nr 5
120-122
EN
The paper deals with an algorithm for Hausdorff dimension estimation based on box-counting dimension calculation. The main goal of the paper is to propose a new approach to box-counting dimension calculation with less computational demands.
PL
W artykule opisano algorytm estymacji wymiaru Hausdorffa oparty o wyznaczanie wymiaru pudełkowego. Głównym celem pracy jest zaproponowanie nowego podejścia do wyznaczania wymiaru pudełkowego, które ma znacznie mniejszą złożoność obliczeniową.
13
Content available remote A Digital Image Encryption Algorithm Based on Hyper-chaotic Cellular Neural Network
Peng J., Zhang D., Liao X.
Fundamenta Informaticae
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2009
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Vol. 90, nr 3
269-282
EN
Using Chaotic characteristics of dynamic system is a promising direction to design cryptosystems that play a pivotal role in a very important engineering application of cognitive informatics, i.e., information assurance and security. However, encryption algorithms based on the lowdimensional chaotic maps face a potential risk of the keystream being reconstructed via return map technique or neural network method. In this paper, we propose a new digital image encryption algorithm that employs a hyper-chaotic cellular neural network. To substantiate its security characteristics, we conduct the following security analyses of the proposed algorithm: key space analysis, sensitivity analysis, information entropy analysis and correlation coefficients analysis of adjacent pixels. The results demonstrate that the proposed encryption algorithm has desirable security properties and can be deployed as a cornerstone in a sound security cryptosystem. The comparison of the proposed algorithm with five other chaos-based image encryption algorithms indicates that our algorithm has a better security performance.
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