No Arabic abstract
In this article we provide the noncommutative Sprott models. We demonstrate, that effectively, each of them is described by system of three complex, ordinary and nonlinear differential equations. Apart of that, we find for such modified models the corresponding (noncommutative) jerk dynamics as well as we study numerically as an example, the deformed Sprott-A system.
In this article we synchronize by active control method all 19 identical Sprott systems provided in paper [10]. Particularly, we find the corresponding active controllers as well as we perform (as an example) the numerical synchronization of two Sprott-A models.
We consider finite approximations of a topological space $M$ by noncommutative lattices of points. These lattices are structure spaces of noncommutative $C^*$-algebras which in turn approximate the algebra $cc(M)$ of continuous functions on $M$. We show how to recover the space $M$ and the algebra $cc(M)$ from a projective system of noncommutative lattices and an inductive system of noncommutative $C^*$-algebras, respectively.
We study the classical dynamics of an axion field (the signal) that is coupling into a Josephson junction (the detector) by means of a capacitive coupling of arbitrary size. Depending on the size of the coupling constant and the initial conditions, we find a rich phase space structure of this nonlinear problem. We present general analytic solutions of the equations of motion in the limit of small amplitudes of the angle variables, and discuss both the case of no dissipation and the case of dissipation in the system. The effect of a magnetic field is investigated as well, leading to topological phase transitions in the phase space structure.
In this paper, we show that the dynamics of a wide variety of nonlinear systems such as engineering, physical, chemical, biological, and ecological systems, can be simulated or modeled by the dynamics of memristor circuits. It has the advantage that we can apply nonlinear circuit theory to analyze the dynamics of memristor circuits. Applying an external source to these memristor circuits, they exhibit complex behavior, such as chaos and non-periodic oscillation. If the memristor circuits have an integral invariant, they can exhibit quasi-periodic or non-periodic behavior by the sinusoidal forcing. Their behavior greatly depends on the initial conditions, the parameters, and the maximum step size of the numerical integration. Furthermore, an overflow is likely to occur due to the numerical instability in long-time simulations. In order to generate a non-periodic oscillation, we have to choose the initial conditions, the parameters, and the maximum step size, carefully. We also show that we can reconstruct chaotic attractors by using the terminal voltage and current of the memristor. Furthermore, in many memristor circuits, the active memristor switches between passive and active modes of operation, depending on its terminal voltage. We can measure its complexity order by defining the binary coding for the operation modes. By using this coding, we show that in the forced memristor Toda lattice equations, the memristors operation modes exhibit the higher complexity. Furthermore, in the memristor Chua circuit, the memristor has the special operation modes.
Recently, there has been provided two chaotic models based on the twist-deformation of classical Henon-Heiles system. First of them has been constructed on the well-known, canonical space-time noncommutativity, while the second one on the Lie-algebraically type of quantum space, with two spatial directions commuting to classical time. In this article, we find the direct link between mentioned above systems, by synchronization both of them in the framework of active control method. Particularly, we derive at the canonical phase-space level the corresponding active controllers as well as we perform (as an example) the numerical synchronization of analyzed models.