By adopting the Adomian decomposition method, the fractional-order Lorenz–Stenflo (LS) system is solved and implemented in a digital signal processor (DSP). The discrete iterative formula of the system is deduced, and a Lyapunov exponent spectrum algorithm is designed. The dynamics of the fractional-order LS system with sets of parameters are analyzed by means of Lyapunov exponent spectra, bifurcation diagrams and 0-1 test. The results illustrate that the fractional-order LS system has rich dynamic behaviors, and both the system parameter and the fractional order can be taken as bifurcation parameters. We implement the fractional-order LS system on a DSP platform. Phase portraits of the fractional-order LS system generated in the DSP agree well with those obtained by computer simulations. This lays a good foundation for the application of the fractional-order LS system.

Corrigendum: Multistable behaviour of coupled Lorenz–Stenflo systems 2014 Phys. Scr. 89 045202

Dynamic analysis and implementation of a digital signal processor of a fractional-order Lorenz-Stenflo system based on the Adomian decomposition method

Certain dynamical systems exhibit sensitivity to initial conditions in which the asymptotic state is selected from multiple possible states. The associated uncertain destination dynamics can be analyzed by an appropriate reduction of the full system to a subsystem that explicitly yields the dynamics [1]. These types of systems are known as multistable systems. In this paper, a scheme for designing delay coupled multistable systems is proposed. The scheme considers delay coupled Lorenz-Stenflo systems. The scheme is based on Lyapunovʼs stability theorem. Numerical simulation results are presented to show the effectiveness of the proposed scheme.

https://iopscience.iop.org/article/10.1088/0031-8949/90/3/035203/pdf

Uncertain destination dynamics of delay coupled systems

In this paper, we propose a scheme for designing discrete extreme multistable systems coupling two identical dynamical systems. Existence of infinitely many attractors in the system is obtained via partial synchronization between two systems for a given set of parameters. We give a conjecture that extreme multistable systems can be designed by coupling two m-dimensional dynamical systems in such a way that i $$(1 \le i\le m-1)$$
 number of state variables of the two systems synchronize completely and $$(m-i)$$
 number of state variables keep constant difference. We demonstrate the applicability of our scheme in two-dimensional (2D) as well as three-dimensional (3D) discrete dynamical systems. In particular, we discuss our scheme taking coupled 2D Henon maps, coupled 2D Duffing maps and coupled 3D Henon maps. We have analytically shown the existence of fixed points and period-2 orbits in the coupled system with the variation of initial conditions. These analytically derived conditions matched very well with the numerical simulation results. Variation of the largest Lyapunov exponent with the initial conditions is shown to confirm the existence of extreme multistability in the model. Our scheme may be useful for designing physically, chemically and biologically useful multistable discrete dynamical systems.

A scheme for designing extreme multistable discrete dynamical systems

http://iopscience.iop.org/article/10.1088/0031-8949/89/10/109401/pdf

Corrigendum: Multistable behaviour of coupled Lorenz–Stenflo systems 2014 Phys. Scr. 89 045202

Citations

Dynamic analysis and implementation of a digital signal processor of a fractional-order Lorenz-Stenflo system based on the Adomian decomposition method

Uncertain destination dynamics of delay coupled systems

A scheme for designing extreme multistable discrete dynamical systems

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Dynamics and transitions of the coupled lorenz system

Erratum to: “Rotating class of parametric resonance processes in coupled oscillators”: [Phys. Lett. A 290 (2001) 288–296]