Monostability,bistability, periodicity and chaos in gene regulatory network

This letter gives a general review on the monostability, bistability, periodicity and chaos in gene regulatory network. Some simple motifs that generate monostability, bistability, periodicity and chaos are analytically and numerically reported. Further research directions of the nonlinear dynamics of gene regulatory network are discussed.     

Multistability and coexisting attractors in a fractional order Coronary artery system

The present study investigates the dynamical properties of a fractional order coronary artery system and its control with uncertainties in the parameters. The fractional order model of the coronary artery system (FOCA) is derived using the Grünwald–Letnikov method and the properties of the FOCA system are discussed. Bifurcation plots of the system in the parameter space are derived and presented. The novelty of the paper is the identification of the multistable feature shown by the FOCA system, which has not been discussed in the research literature. Various coexisting attractors are also presented to show the multistability. An adaptive sliding mode controller is designed to stabilize the chaotic oscillations in the FOCA system. Numerical simulations are conducted to indicate the effectiveness of the controller.     

A new 4D chaotic system with hidden attractor and its engineering applications: Analog circuit design and field programmable gate array implementation

Nowadays, designing chaotic systems with hidden attractor is one of the most interesting topics in nonlinear dynamics and chaos. In this paper, a new 4D chaotic system is proposed. This new chaotic system has no equilibria, and so it belongs to the category of systems with hidden attractors. Dynamical features of this system are investigated with the help of its state-space portraits, bifurcation diagram, Lyapunov exponents diagram, and basin of attraction. Also a hardware realisation of this system is proposed by using field programmable gate arrays (FPGA). In addition, an electronic circuit design for the chaotic system is introduced.     

Chaos-based application of a novel no-equilibrium chaotic system with coexisting attractors

Nonlinear Dynamics - Novel chaotic system designs and their engineering applications have received considerable critical attention. In this paper, a new three-dimensional chaotic system and its...     

An adaptive observer synchronization using chaotic time-delay system for secure communication

Nonlinear Dynamics - Recently, the time delay has considerable attention in the existence of chaos in the nonlinear dynamical systems. In this paper, we therefore develop a new cascade-coupled...     

A Hopfield neural network with multiple attractors and its FPGA design

Neural network is important for a wide range of applications. Especially, a small neural network can display various complex behaviors. In this work, the investigations of a Hopfield neural network and its field programmable gate array (FPGA) implementation have been reported. The considered Hopfield neural network is simple because it includes only three neurons. It is interesting that we observed chaos and numerous coexisting attractors in such a network. In addition, the network has been implemented via an FPGA platform to verify its feasibility.     

A fractional map with hidden attractors: chaos and control

The European Physical Journal Special Topics - This paper studies the dynamics of a new fractional-order map with no fixed points. Through phase plots, bifurcation diagrams, largest Lyapunov...