In this paper, a fractional-order model of a financial risk dynamical system is proposed and the ... more In this paper, a fractional-order model of a financial risk dynamical system is proposed and the complex behavior of such a system is presented. The basic dynamical behavior of this financial risk dynamic system, such as chaotic attractor, Lyapunov exponents, and bifurcation analysis, is investigated. We find that numerical results display periodic behavior and chaotic behavior of the system. The results of theoretical models and numerical simulation are helpful for better understanding of other similar nonlinear financial risk dynamic systems. Furthermore, the adaptive fuzzy control for the fractional-order financial risk chaotic system is investigated on the fractional Lyapunov stability criterion. Finally, numerical simulation is given to confirm the effectiveness of the proposed method.
TELKOMNIKA Telecommunication Computing Electronics and Control, 2019
Chaos theory has several applications in science and engineering. In this work, we announce a new... more Chaos theory has several applications in science and engineering. In this work, we announce a new two-scroll chaotic system with two nonlinearities. The dynamical properties of the system such as dissipativity, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension and bifurcation diagram are explored in detail. The presence of coexisting chaotic attractors, coexisting chaotic and periodic attractors in the system is also investigated. In addition, the offset boosting of a variable in the new chaotic system is achieved by adding a single controlled constant. It is shown that the new chaotic system has rotation symmetry about the z-axis. An electronic circuit simulation of the new two-scroll chaotic system is built using Multisim to check the feasibility of the theoretical model. 1. Introduction In the last few decades, many advances applications of chaotic systems have been actively carried out in the literature [1-4]. Classical examples of 3-D chaotic systems include the Lorenz system [5], Rössler system [6], Chen system [7], Lü system [8], Liu system [9], Tigan system [10], Sprott systems [11], Arneodo system [12], etc. Chaotic systems arise in many applications of nonlinear oscillators [13-18]. Vaidyanathan [13] used active control method for the global chaos synchronization of the forced Van der Pol chaotic oscillators. Ghosh et al. [14] discussed the generation and control of chaos in a single loop optoelectronic oscillator with the variation of feedback loop delay. Vaidyanathan and Rasappan [15] applied nonlinear control for achieving hybrid synchronization of hyperchaotic Qi and Lü oscillators. Jin [16] presented a digitally programmable multi-direction fully integrated chaotic oscillator. Vaidyanathan [17] derived new results for the adaptive controller and synchronizer design for the Qi-Chen chaotic oscillator. Vaidyanathan [18] discussed the qualitative analysis, control and synchronization of a ten-term 4-D hyperchaotic system with an exponential nonlinearity and three quadratic nonlinearities. Chaotic systems have applications in artificial and cellular neural networks [19, 20]. Akhmet and Fen [19] discussed the generation of cyclic and toroidal chaos by Hopfield neural networks. Vaidyanathan [20] derived new results for the synchronization of 3-cells cellular neural network (CNN) attractors via adaptive control method. Chaotic systems have applications in biology and medicine [21-24]. Akaishi et al. [21] presented a new theoretical model from a viewpoint of complex system with chaos model to reproduce and explain the non-linear clinical and pathological manifestations in multiple sclerosis. Vaidyanathan [22] presented new results for the adaptive control of the FitzHugh-Nagumo chaotic neuron model. Vaidyanathan [23] used backstepping control for the control and synchronization of a novel jerk system with two quadratic nonlinearities. Shepelev et al. [24] discussed the bifurcations of spatiotemporal structures in a medium of FitzHugh-Nagumo neurons with diffusive coupling.
This paper reports the finding a new chaotic system with a conch-shaped equilibrium curve. The pr... more This paper reports the finding a new chaotic system with a conch-shaped equilibrium curve. The proposed system is a new addition to existing chaotic systems with closed curves of equilibrium points in the literature. Lyapunov exponents of the new chaotic system are studiedfor verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. An electronic circuit simulation of the new chaotic system with conch-shaped equilibrium curve is shown using MultiSIM to check the model feasibility.
This paper reports the finding a new four-scroll chaotic system with four nonlinearities. The pro... more This paper reports the finding a new four-scroll chaotic system with four nonlinearities. The proposed system is a new addition to existing multi-scroll chaotic systems in the literature. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. As the new four-scroll chaotic system is shown to have three unstable equilibrium points, it has a self-excited chaotic attractor. An electronic circuit simulation of the new four-scroll chaotic system is shown using MultiSIM to check the feasibility of the four-scroll chaotic model.
Jerk systems are popular in mechanical engineering and chaotic jerk systems are used in many appl... more Jerk systems are popular in mechanical engineering and chaotic jerk systems are used in many applications as they have simple structure and complex dynamic properties. In this work, we report a new chaotic jerk system with three nonlinear terms. Dynamical properties of the chaotic jerk system are analyzed through equilibrium analysis, dissipativity, phase portraits and Lyapunov chaos exponents. We show that the new chaotic jerk system has a unique saddle-focus equilibrium at the origin. Thus, the new chaotic jerk system has a self-excited strange attractor. Next, global chaos synchronization of a pair of new chaotic jerk systems is successfully achieved via adaptive backstepping control.
In the chaos literature, there is currently significant interest in the discovery of new chaotic ... more In the chaos literature, there is currently significant interest in the discovery of new chaotic systems with hidden chaotic attractors. A new 4-D chaotic system with only two quadratic nonlinearities is investigated in this work. First, we derive a no-equilibrium chaotic system and show that the new chaotic system exhibits hidden attractor. Properties of the new chaotic system are analyzed by means of phase portraits, Lyapunov chaos exponents, and Kaplan-Yorke dimension. Then an electronic circuit realization is shown to validate the chaotic behavior of the new 4-D chaotic system. Finally, the physical circuit experimental results of the 4-D chaotic system show agreement with numerical simulations.
In recent decades, hyperjerk systems have been studied well in the literature because of their si... more In recent decades, hyperjerk systems have been studied well in the literature because of their simple dynamics structure and complex qualitative properties. In this work, we announce a new hyperchaotic hyperjerk system with three nonlinear terms. Dynamical properties of the hyperjerk system are analyzed through equilibrium analysis, dissipativity, phase portraits and Lyapunov chaos exponents. We show that the new hyperchaotic hyperjerk system has a unique saddle-focus equilibrium at the origin. Thus, the new hyperchaotic hyperjerk system has a self-excited strange attractor. Next, global hyperchaos synchronization of a pair of new hyperchaotic hyperjerk systems is successfully achieved via adaptive backstepping control. Also, an electronic circuit of the hyperchaotic hyperjerk system has been designed via MultiSIM to check the feasibility of the theoretical system.
Modelling and control applications of dynamical systems in chaos theory arising in several areas ... more Modelling and control applications of dynamical systems in chaos theory arising in several areas are investigated and new control techniques are designed in the chaos literature. We propose a new complex finance chaotic model with states as the interest rate, investment demand, and price index. In this work, after studying the dynamical properties of the new finance model, an electronic chaotic circuit of the model is realized in Multisim. Based on passive control theory, we derive a new controller for globally synchronizing state trajectories of the new finance models. Using the new finance chaotic model developed in this work, a new voice encryption algorithm design is presented. With the proposed algorithm, voice encryption application is performed, and results are described.
International Journal of Electrical and Computer Engineering (IJECE)
This paper reports the finding a new chaotic system with a pear-shaped equilibrium curve and make... more This paper reports the finding a new chaotic system with a pear-shaped equilibrium curve and makes a valuable addition to existing chaotic systems with infinite equilibrium points in the literature. The new chaotic system has a total of five nonlinearities. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system are unveiled. An electronic circuit simulation of the new chaotic system with pear-shaped equilibrium curve is shown using Multisim to check the model feasibility.
In this paper, a fractional-order model of a financial risk dynamical system is proposed and the ... more In this paper, a fractional-order model of a financial risk dynamical system is proposed and the complex behavior of such a system is presented. The basic dynamical behavior of this financial risk dynamic system, such as chaotic attractor, Lyapunov exponents, and bifurcation analysis, is investigated. We find that numerical results display periodic behavior and chaotic behavior of the system. The results of theoretical models and numerical simulation are helpful for better understanding of other similar nonlinear financial risk dynamic systems. Furthermore, the adaptive fuzzy control for the fractional-order financial risk chaotic system is investigated on the fractional Lyapunov stability criterion. Finally, numerical simulation is given to confirm the effectiveness of the proposed method.
TELKOMNIKA Telecommunication Computing Electronics and Control, 2019
Chaos theory has several applications in science and engineering. In this work, we announce a new... more Chaos theory has several applications in science and engineering. In this work, we announce a new two-scroll chaotic system with two nonlinearities. The dynamical properties of the system such as dissipativity, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension and bifurcation diagram are explored in detail. The presence of coexisting chaotic attractors, coexisting chaotic and periodic attractors in the system is also investigated. In addition, the offset boosting of a variable in the new chaotic system is achieved by adding a single controlled constant. It is shown that the new chaotic system has rotation symmetry about the z-axis. An electronic circuit simulation of the new two-scroll chaotic system is built using Multisim to check the feasibility of the theoretical model. 1. Introduction In the last few decades, many advances applications of chaotic systems have been actively carried out in the literature [1-4]. Classical examples of 3-D chaotic systems include the Lorenz system [5], Rössler system [6], Chen system [7], Lü system [8], Liu system [9], Tigan system [10], Sprott systems [11], Arneodo system [12], etc. Chaotic systems arise in many applications of nonlinear oscillators [13-18]. Vaidyanathan [13] used active control method for the global chaos synchronization of the forced Van der Pol chaotic oscillators. Ghosh et al. [14] discussed the generation and control of chaos in a single loop optoelectronic oscillator with the variation of feedback loop delay. Vaidyanathan and Rasappan [15] applied nonlinear control for achieving hybrid synchronization of hyperchaotic Qi and Lü oscillators. Jin [16] presented a digitally programmable multi-direction fully integrated chaotic oscillator. Vaidyanathan [17] derived new results for the adaptive controller and synchronizer design for the Qi-Chen chaotic oscillator. Vaidyanathan [18] discussed the qualitative analysis, control and synchronization of a ten-term 4-D hyperchaotic system with an exponential nonlinearity and three quadratic nonlinearities. Chaotic systems have applications in artificial and cellular neural networks [19, 20]. Akhmet and Fen [19] discussed the generation of cyclic and toroidal chaos by Hopfield neural networks. Vaidyanathan [20] derived new results for the synchronization of 3-cells cellular neural network (CNN) attractors via adaptive control method. Chaotic systems have applications in biology and medicine [21-24]. Akaishi et al. [21] presented a new theoretical model from a viewpoint of complex system with chaos model to reproduce and explain the non-linear clinical and pathological manifestations in multiple sclerosis. Vaidyanathan [22] presented new results for the adaptive control of the FitzHugh-Nagumo chaotic neuron model. Vaidyanathan [23] used backstepping control for the control and synchronization of a novel jerk system with two quadratic nonlinearities. Shepelev et al. [24] discussed the bifurcations of spatiotemporal structures in a medium of FitzHugh-Nagumo neurons with diffusive coupling.
This paper reports the finding a new chaotic system with a conch-shaped equilibrium curve. The pr... more This paper reports the finding a new chaotic system with a conch-shaped equilibrium curve. The proposed system is a new addition to existing chaotic systems with closed curves of equilibrium points in the literature. Lyapunov exponents of the new chaotic system are studiedfor verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. An electronic circuit simulation of the new chaotic system with conch-shaped equilibrium curve is shown using MultiSIM to check the model feasibility.
This paper reports the finding a new four-scroll chaotic system with four nonlinearities. The pro... more This paper reports the finding a new four-scroll chaotic system with four nonlinearities. The proposed system is a new addition to existing multi-scroll chaotic systems in the literature. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. As the new four-scroll chaotic system is shown to have three unstable equilibrium points, it has a self-excited chaotic attractor. An electronic circuit simulation of the new four-scroll chaotic system is shown using MultiSIM to check the feasibility of the four-scroll chaotic model.
Jerk systems are popular in mechanical engineering and chaotic jerk systems are used in many appl... more Jerk systems are popular in mechanical engineering and chaotic jerk systems are used in many applications as they have simple structure and complex dynamic properties. In this work, we report a new chaotic jerk system with three nonlinear terms. Dynamical properties of the chaotic jerk system are analyzed through equilibrium analysis, dissipativity, phase portraits and Lyapunov chaos exponents. We show that the new chaotic jerk system has a unique saddle-focus equilibrium at the origin. Thus, the new chaotic jerk system has a self-excited strange attractor. Next, global chaos synchronization of a pair of new chaotic jerk systems is successfully achieved via adaptive backstepping control.
In the chaos literature, there is currently significant interest in the discovery of new chaotic ... more In the chaos literature, there is currently significant interest in the discovery of new chaotic systems with hidden chaotic attractors. A new 4-D chaotic system with only two quadratic nonlinearities is investigated in this work. First, we derive a no-equilibrium chaotic system and show that the new chaotic system exhibits hidden attractor. Properties of the new chaotic system are analyzed by means of phase portraits, Lyapunov chaos exponents, and Kaplan-Yorke dimension. Then an electronic circuit realization is shown to validate the chaotic behavior of the new 4-D chaotic system. Finally, the physical circuit experimental results of the 4-D chaotic system show agreement with numerical simulations.
In recent decades, hyperjerk systems have been studied well in the literature because of their si... more In recent decades, hyperjerk systems have been studied well in the literature because of their simple dynamics structure and complex qualitative properties. In this work, we announce a new hyperchaotic hyperjerk system with three nonlinear terms. Dynamical properties of the hyperjerk system are analyzed through equilibrium analysis, dissipativity, phase portraits and Lyapunov chaos exponents. We show that the new hyperchaotic hyperjerk system has a unique saddle-focus equilibrium at the origin. Thus, the new hyperchaotic hyperjerk system has a self-excited strange attractor. Next, global hyperchaos synchronization of a pair of new hyperchaotic hyperjerk systems is successfully achieved via adaptive backstepping control. Also, an electronic circuit of the hyperchaotic hyperjerk system has been designed via MultiSIM to check the feasibility of the theoretical system.
Modelling and control applications of dynamical systems in chaos theory arising in several areas ... more Modelling and control applications of dynamical systems in chaos theory arising in several areas are investigated and new control techniques are designed in the chaos literature. We propose a new complex finance chaotic model with states as the interest rate, investment demand, and price index. In this work, after studying the dynamical properties of the new finance model, an electronic chaotic circuit of the model is realized in Multisim. Based on passive control theory, we derive a new controller for globally synchronizing state trajectories of the new finance models. Using the new finance chaotic model developed in this work, a new voice encryption algorithm design is presented. With the proposed algorithm, voice encryption application is performed, and results are described.
International Journal of Electrical and Computer Engineering (IJECE)
This paper reports the finding a new chaotic system with a pear-shaped equilibrium curve and make... more This paper reports the finding a new chaotic system with a pear-shaped equilibrium curve and makes a valuable addition to existing chaotic systems with infinite equilibrium points in the literature. The new chaotic system has a total of five nonlinearities. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system are unveiled. An electronic circuit simulation of the new chaotic system with pear-shaped equilibrium curve is shown using Multisim to check the model feasibility.
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Papers by Aceng Sambas