Applications of chaos theory to the molecular biology of aging

Kyriazis, Marios

doi:10.1016/0531-5565(91)90074-v

Cited by 68 publications

(27 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The novel circulant highly chaotic systems (53) and (54) with unknown system parameters are globally and exponentially synchronized for all initial conditions by the adaptive control law (59) and the parameter update law (66), where k 1 , k 2 , k 3 are positive gain constants and F, G are defined by the Eqs. (52) and (57), respectively.…”

Section: Theoremmentioning

confidence: 99%

“…Some commonly known applications are oscillators [40,41], lasers [42,43], chemical reactions [44][45][46][47][48][49][50][51], biology [52][53][54][55][55][56][57][58][59][60][61], ecology [62,63], encryption [64,65], cryptosystems [66,67], mechanical systems [68][69][70][71][72], secure communications [73][74][75], robotics [76][77][78], cardiology [79,80], intelligent control [81,82], neural networks [83][84][85], finance [86,87], memristors [88,…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Novel 3-D Circulant Highly Chaotic System with Labyrinth Chaos

Vaidyanathan

2016

Advances in Chaos Theory and Intelligent Control

View full text Add to dashboard Cite

In this work, we describe a novel 3-D circulant highly chaotic system with labyrinth chaos. The novel chaotic system is a nine-term polynomial system with six sinusoidal nonlinearities. The phase portraits of the novel circulant chaotic system are illustrated and the dynamic properties of the novel circulant chaotic system are discussed. The novel circulant chaotic system has infinitely many equilibrium points and it exhibits labyrinth chaos. We show that all the equilibrium points of the novel circulant chaotic system are saddle-foci and hence they are unstable. The Lyapunov exponents of the novel circulant chaotic system are obtained as L 1 = 10.3755, L 2 = 0 and L 3 = −10.4113. Thus, the Maximal Lyapunov Exponent (MLE) of the novel chaotic system is obtained as L 1 = 10.3755, which is a large value. This shows that the novel 3-D circulant chaotic system is highly chaotic. Also, the Kaplan-Yorke dimension of the novel circulant highly chaotic system is obtained as D K Y = 2.9966. Since the Kaplan-Yorke dimension of the the novel circulant chaotic system has a large value and close to three, the novel circulant chaotic system with labyrinth chaos exhibits highly complex behaviour. Since the sum of the Lyapunov exponents is negative, the novel chaotic system is dissipative. Next, we derive new results for the global chaos control of the novel circulant highly chaotic system with unknown parameters using adaptive control method. We also derive new results for the global chaos synchronization of the identical novel circulant highly chaotic systems with unknown parameters using adaptive control method. The main control results are established using Lyapunov stability theory. MATLAB simulations are depicted to illustrate the phase portraits of the novel circulant highly chaotic system and also the adaptive control results derived in this work.

show abstract

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Novel 3-D Circulant Highly Chaotic System with Labyrinth Chaos

Vaidyanathan

2016

Advances in Chaos Theory and Intelligent Control

View full text Add to dashboard Cite

show abstract

“…Some important applications can be mentioned as oscillators [18,44], lasers [22,67], chemical reactions [11,33], cryptosystems [37,55], secure communications [9,29,68], biology [8,20], ecology [12,48], robotics [30,62], cardiology [34,64], neural networks [15,17], finance [13,47], etc.…”

Section: Introductionmentioning

confidence: 99%

Backstepping Controller Design for the Global Chaos Synchronization of Sprott’s Jerk Systems

Vaidyanathan

Idowu

Azar

2014

Chaos Modeling and Control Systems Design

108

View full text Add to dashboard Cite

This research work investigates the global chaos synchronization of Sprott's jerk chaotic system using backstepping control method. Sprott's jerk system (1997) is algebraically the simplest dissipative chaotic system consisting of five terms and a quadratic nonlinearity. Sprott's chaotic system involves only five terms and one quadratic nonlinearity, while Rössler's chaotic system (1976) involves seven terms and one quadratic nonlinearity. This work first details the properties of the Sprott's jerk chaotic system. The phase portraits of the Sprott's jerk system are described. The Lyapunov exponents of the Sprott's jerk system are obtained as L 1 = 0.0525, L 2 = 0 and L 3 = −2.0727. The Lyapunov dimension of the Sprott's jerk system is obtained as D L = 2.0253. Next, an active backstepping controller is designed for the global chaos synchronization of identical Sprott's jerk systems with known 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 chaotic systems. Finally, an adaptive backstepping controller is designed for the global chaos synchronization of identical Sprott's jerk systems with unknown parameters. MATLAB simulations are provided to validate and demonstrate the effectiveness of the proposed active and adaptive chaos synchronization schemes for the Sprott's jerk systems.

show abstract

“…Some well-known paradigms of 3-D chaotic systems are Arneodo system [8], Sprott systems [9], Chen system [10], Lü-Chen system [11], Liu system [12], Cai system [13], T-system [14] Chaos theory has applications in several fields of science and engineering such as oscillators [33,34], chemical reactions [35,36], biology [37,38], ecology [39,40], neural networks [41,42], gyros [43], Tokamak system [44,45],neurology [46,47,48], circuits [49,50], etc.…”

Section: Introductionmentioning

confidence: 99%

Hyperchaos, adaptive control and synchronization of a novel 4-D hyperchaotic system with two quadratic nonlinearities

Vaidyanathan¹

2016

Archives of Control Sciences

View full text Add to dashboard Cite

Hyperchaos, adaptive control and synchronization of a novel 4-D hyperchaotic system with two quadratic nonlinearities SUNDARAPANDIAN VAIDYANATHAN This research work announces an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. We describe the qualitative properties of the novel 4-D hyperchaotic system and illustrate their phase portraits. We show that the novel 4-D hyperchaotic system has two unstable equilibrium points. The novel 4-D hyperchaotic system has the Lyapunov exponents L 1 = 3.1575, L 2 = 0.3035, L 3 = 0 and L 4 = −33.4180. The Kaplan-Yorke dimension of this novel hyperchaotic system is found as D KY = 3.1026. Since the sum of the Lyapunov exponents of the novel hyperchaotic system is negative, we deduce that the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to stabilize the novel 4-D hyperchaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 4-D hyperchaotic systems with unknown system parameters. The adaptive control results are established using Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results derived in this research work.

show abstract

Applications of chaos theory to the molecular biology of aging

Cited by 68 publications

References 3 publications

A Novel 3-D Circulant Highly Chaotic System with Labyrinth Chaos

A Novel 3-D Circulant Highly Chaotic System with Labyrinth Chaos

Backstepping Controller Design for the Global Chaos Synchronization of Sprott’s Jerk Systems

Hyperchaos, adaptive control and synchronization of a novel 4-D hyperchaotic system with two quadratic nonlinearities

Contact Info

Product

Resources

About