Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with  Hyperboli c Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters

Vaidyanathan, Sundarapandian

doi:10.25103/jestr.064.07

Cited by 87 publications

(5 citation statements)

References 43 publications

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“…Many new chaotic systems have been also discovered like Li system [18], Sundarapandian systems [19,20], Vaidyanathan systems [21,22,23,24,25,26,27,28], Pehlivan system [29], Jafari system [30], Pham system [31], etc.…”

Section: Introductionmentioning

confidence: 98%

Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation

Vaidyanathan¹,

Volos²,

Pham³

2014

Archives of Control Sciences

100

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In this research work, a twelve-term novel 5-D hyperchaotic Lorenz system with three quadratic nonlinearities has been derived by adding a feedback control to a ten-term 4-D hyperchaotic Lorenz system with three quadratic nonlinearities. The 4-D hyperchaotic Lorenz system has the Lyapunov exponents L 1 = 0.3684, L 2 = 0.2174, L 3 = 0 and L 4 = −12.9513, and the Kaplan-Yorke dimension of this 4-D system is found as D KY = 3.0452. The 5-D novel hyperchaotic Lorenz system proposed in this work has the Lyapunov exponents L 1 = 0.4195, L 2 = 0.2430, L 3 = 0.0145, L 4 = 0 and L 5 = −13.0405, and the Kaplan-Yorke dimension of this 5-D system is found as D KY = 4.0159. Thus, the novel 5-D hyperchaotic Lorenz system has a maximal Lyapunov exponent (MLE), which is greater than the maximal Lyapunov exponent (MLE) of the 4-D hyperchaotic Lorenz system. The 5-D novel hyperchaotic Lorenz system has a unique equilibrium point at the origin, which is a saddle-point and hence unstable. Next, an adaptive controller is designed to stabilize the novel 5-D hyperchaotic Lorenz system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 5-D hyperchaotic Lorenz systems with unknown system parameters. Finally, an electronic circuit realization of the novel 5-D hyperchaotic Lorenz system using SPICE is described in detail to confirm the feasibility of the theoretical model.

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Section: Introductionmentioning

confidence: 98%

Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation

Vaidyanathan¹,

Volos²,

Pham³

2014

Archives of Control Sciences

100

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“…In Meyer-Bäse et al (1996), the CNN concept was extended to the case of different time-scale systems with two types of state variables, that is, short-term memory (STM) and long-term memory (LTM), that describe the fast neural activity and the slow unsupervised synoptic modification, respectively. In the last decades, CNNs have great application value in many areas such as secure communication, biological system, and information processing (Liao and Huang, 1999; Ren et al, 2020; Strogatz and Stewart, 1993; Vaidyanathan, 2013; Vaseghi et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Predefined-time synchronization of competitive neural networks with deterministic disturbances and stochastic noises

Garza-Alonso

Rodriguez‐Ramirez

2023

Transactions of the Institute of Measurement and Control

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This paper presents the drive-response synchronization problem for competitive neural networks in predefined time. The response system is considered in the presence of deterministic disturbances satisfying Lipschitz conditions and in the presence of both stochastic white noises and deterministic disturbances satisfying Lipschitz conditions. The effect of deterministic disturbances and stochastic noises is suppressed by designing a linear time-varying continuous control input driving the synchronization errors at the origin for an a priori predefined time, independently of initial conditions, deterministic disturbances, and stochastic noises. Finally, numerical simulations are conducted to demonstrate validity of the obtained theoretical results. The conducted comparisons with other predefined-time convergent synchronization algorithms reveal better performance of the proposed synchronization technique.

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“…Chaos encryption has an elevation sensitivity to the initial value and therefore it has a great area for application [2]. The chaotic demeanor of effective systems can be applied in numerous realism implementations, for example, but not limited to oscillators [3], physics [4], random bit generators [5], Plasma systems [6], Tokamak chaotic systems [7], biomedical and medical applications [8], secure communications [9], optoelectronic devices [10], memristors [11]. The chaos-based communication systems have appealed a large interest, start with Shannon's 1947 admission that a noise-like signal with a waveform of maximal entropy produced an optimization wireless communications channel capacity [12].…”

Section: Introductionmentioning

confidence: 99%

“…The chaos-based communication systems have appealed a large interest, start with Shannon's 1947 admission that a noise-like signal with a waveform of maximal entropy produced an optimization wireless communications channel capacity [12]. Numerous novel chaotic systems that offer various dynamical actions have possessed a place in literature [10,[13][14][15][16][17][18][19][20][21]. Wireless chaotic communication has many features other than the systems dependent on a classical harmonic signal, viz enormous safety and hide information advantages [22], weak power spectrum intensity, resistance to multipath fading, is simply implemented for broadband communication system [23], and sensitivity to initial conditions [8,[24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

International Journal of Electronics and Telecommunications

Salih

2021

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Chaos is an active topic of study in the field of secure communication systems that have garnered much consideration in recent years because of excessive sensitivity to a simple change in its initial conditions. In this paper, the essential features of the suggested WINDMI chaotic system like the phase portraits of the attractors, bifurcation, PSD, correlation, and balance property of the windmi chaotic system have been depicted in detail through MATLAB tools simulations and circuital application. The bifurcation examination detects a wealthy and attractive characteristic of the proposed windmi chaotic oscillator such as periodical multiple bifurcations, has two stable states chaotic demeanor, periodical windows, and recapture bifurcations. In this paper, after exploring the dynamic features of the windmi chaos paradigm, a practical chaotic circuit is implemented on the fpaa chip. Eventually, the circuit practical results of the windmi chaotic attractors present similarities with numerical simulations. The importance of the work is reflected in the use of field programmable analog array in the implementation of the windmi oscillator, and the possibility of varying the initial condition during the operation of the system. An unlimited number of signals can be generated, which enables it to be used as an oscillator utilized in many transceiver systems, that utilized an unlimited number of signals.

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Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperboli c Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters

Cited by 87 publications

References 43 publications

Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation

Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation

Predefined-time synchronization of competitive neural networks with deterministic disturbances and stochastic noises

International Journal of Electronics and Telecommunications

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