Chaotic systems without equilibrium points have been investigated and received significant attention recently. In this work, we propose a new three-dimensional fractional-order chaotic system without equilibrium. Dynamics of the fractional-order system are investigated and a circuit implementation of the system by using electronic components is presented. Interestingly, bistable chaotic attractors of such fractional system are discovered. In addition, we are able to control and synchronize the system by using active control and unidirectional coupling.

A simple three-dimensional fractional-order chaotic system without equilibrium: Dynamics, circuitry implementation, chaos control and synchronization

A survey on the integrated design of chaotic oscillators

Recent evidence suggests that there exists chaos in a few no-equilibrium systems A chaotic system without equilibrium is proposed and studied in this work It is worth noting that due to the absence of equilibrium, such a system belongs to a class of systems with hidden attractor Dynamics properties and the feasibility of the system are investigated by using numerical simulations and circuit implementation Interestingly, this no-equilibrium system has one variable with the freedom of offset boosting

Dynamics and circuit realization of a no-equilibrium chaotic system with a boostable variable

We study the synchronization of a piecewise linear function-based chaotic system. That system generates multiple scrolls in multiple directions (two- and three-directions) on phase space. In this scenario, the design of a controller based on Generalized Hamiltonian forms is possible. As function of control signals, we propose a master–slave synchronization scheme using 2
 n
 −1 combinations to drive a nonlinear state observer. Associated with this, the piecewise linear functions of the slave are directly controlled by the state-variables of the master system. We computed the synchronization error for each combinations. Besides, the circuit synthesis based on operational amplifiers validates our synchronization scheme by means of SPICE simulations. We observed that the synchronization error at circuit level depends on the number of the control signals used. Our numerical and SPICE simulation results are in agreement showing the usefulness of the proposed approach.

Synchronization of PWL function-based 2D and 3D multi-scroll chaotic systems

In this work, we proposed a voltage-to-current cell based on a Complementary metal-oxide-semiconductor (CMOS) inverter designed by using floating gate transistors. We demonstrate its usefulness for the design of stair-type and sawtooth functions to be used in the implementation of a multiscroll chaotic oscillator. The main advantage of using floating gate transistors to design the nonlinear functions is the elimination of external reference DC sources, as is typically done in most of the nonlinear functions that generate multiscroll attractors. The key guidelines for the design of our proposed voltage-to-current cell are given to provide good performances in the design of an integrated multiscroll chaotic oscillator. HSPICE simulations are presented to demonstrate the usefulness of the proposed cell to generate multiscroll attractors. Finally, simulation results before and after layout are presented to show the good agreement with respect to theoretical results. HSPICE simulations of the post-layout design are in accordance with the system behavior. Copyright © 2011 John Wiley & Sons, Ltd.

Esteban Tlelo Cuautle

Papers

Electronic Design Automation of Multi-Scroll Chaos Generators