Complex dynamics in a quasi-periodic plasma perturbations model

Abstract

In this paper, the complex dynamics of a quasi-periodic plasma perturbations (QPP) model, which governs the interplay between a driver associated with pressure gradient and relaxation of instability due to magnetic field perturbations in Tokamaks, are studied. The model consists of three coupled ordinary differential equations (ODEs) and contains three parameters. This paper consists of three parts: (1) We study the stability and bifurcations of the QPP model, which gives the theoretical interpretation of various types of oscillations observed in [Phys. Plasmas, 18(2011):1-7]. In particular, assuming that there exists a finite time lag τ between the plasma pressure gradient and the speed of the magnetic field, we also study the delay effect in the QPP model from the point of view of Hopf bifurcation. (2) We provide some numerical indices for identifying chaotic properties of the QPP system, which shows that the QPP model has chaotic behaviors for a wide range of parameters. Then we prove that the QPP model is not rationally integrable in an extended Liouville sense for almost all parameter values, which may help us distinguish values of parameters for which the QPP model is integrable. (3) To understand the asymptotic behavior of the orbits for the QPP model, we also provide a complete description of its dynamical behavior at infinity by the Poincaré compactification method. Our results show that the input power h and the relaxation of the instability δ do not affect the global dynamics at infinity of the QPP model and the heat diffusion coefficient η just yield quantitative, but not qualitative changes for the global dynamics at infinity of the QPP model.

Nuclear fusion and nuclear fusion materials

“…Tokamak is a kind of annular container which uses magnetic confinement to realize controlled nuclear fusion. Its name Tokamak comes from ring, vacuum chamber, magnet and coil [1]. It was originally invented by Azimovich and others of Kurchatov Institute in Moscow, Soviet Union in 1950s.…”

Complex Dynamics and Chaos Control of a Discrete-Time Predator-Prey Model

“…Te area of discrete-time systems analysis has made great strides in comprehending the complicated dynamics shown by many systems. Classic works in this area, such as the discretized quasiperiodic plasma perturbations model [4,5], the discretized fractional-order predator-prey system [6][7][8], the discrete economic system [9][10][11], and discrete systems describing competition games [12][13][14], have all played important roles in unraveling the complexities of discrete systems. Tese seminal studies have aided understanding of phenomena such as the emergence of complex patterns and bifurcations in plasma oscillations, the impact of fractional-order dynamics on predator-prey population dynamics, the nonlinear dynamics underlying economic systems, and the intricate dynamics of competitive interactions.…”