Study of new chaotic flows on a family of 3-dimensional systems with quadratic nonlinearities

In this paper, a new three-dimensional chaotic system with two exponential nonlinearities is presented. The analysis of fixed points of the proposed system suggests existence of one hyperbolic index-2 spiral saddle-type fixed point. The proposed system fulfils Shilnikov criterion and nature of the chaos is found to be dissipative. Bifurcation diagrams, maximum Lyapunov exponents and Kaplan–Yorke dimension are examined through numerical simulations to investigate dynamics of proposed system. The hardware feasibility of the proposed system is illustrated through current feedback operational amplifier (CFOA)-based circuit implementation. The proposed circuit uses six CFOAs, two diodes to establish nonlinearity, eleven resistors and three capacitors. The absence of analog multiplier in the proposed circuit makes it superior to the existing counterpart in the sense that it does not require area and power-consuming active building block. To confirm the chaotic nature of the proposed circuit, LTspice simulations are done to obtain phase portraits which are found to be strange attractors and are topologically different from the shape of the existing attractors. Moreover, we have investigated the synchronization of the proposed chaotic system using adaptive control scheme and proposed CFOA-based complete circuit design of the adaptively synchronized system. Also, the effect of the tolerance of passive components and temperature on the behavior of the proposed chaotic circuit and the complete synchronization circuit has also been studied. It is found that the circuit is sensitive to the value of resistors and temperature to an extent and can work properly within their limits.

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Puntos de equilibrio asintóticamente estables en nuevos sistemas caóticos

Casas-García

Quezada-Téllez

Carrillo-Moreno

et al. 2016

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En este trabajo se presentan 10 nuevos sistemas autónomos no lineales caóticos simples. Estos sistemas se encontraron utilizando el método Monte Carlo y tienen la característica de tener uno de sus puntos de equilibrio asintóticamente estables. Estos nuevos sistemas no tienen caos en el sentido de Shilnikov, pero sus diagramas de bifurcación muestran una ruta de periodo doble hacia el caos. Se calculó también la dimensión de Kaplan-Yorke, dando como resultado en un rango de 2-3.

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Study of new chaotic flows on a family of 3-dimensional systems with quadratic nonlinearities

Cited by 3 publications

References 8 publications

A chemical representation of a chaotic system with a unique stable equilibrium point

A chemical representation of a chaotic system with a unique stable equilibrium point

A Novel Chaotic System with Exponential Nonlinearity and its Adaptive Self-Synchronization: From Numerical Simulations to Circuit Implementation

Puntos de equilibrio asintóticamente estables en nuevos sistemas caóticos

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