Pseudoinversion Fractals

In this paper, we present some modifications of inversion fractals. The first modification is based on the use of different metrics in the inversion transformation. Moreover, we propose a switching process between different metric spaces. All the proposed modifications allowed us to obtain new and diverse fractal patterns that differ from the original inversion fractals

Attainability analysis in the problem of stochastic equilibria synthesis for nonlinear discrete systems

A nonlinear discrete-time control system forced by stochastic disturbances is considered. We study the problem of synthesis of the regulator which stabilizes an equilibrium of the deterministic system and provides required scattering of random states near this equilibrium for the corresponding stochastic system. Our approach is based on the stochastic sensitivity functions technique. The necessary and important part of the examined control problem is an analysis of attainability. For 2D systems, a detailed investigation of attainability domains is given. A parametrical description of the attainability domains for various types of control inputs in a stochastic Henon model is presented. Application of this technique for suppression of noise-induced chaos is demonstrated

Methods of Stochastic Analysis of Complex Regimes in the 3D Hindmarsh-Rose Neuron Model

A problem of the stochastic nonlinear analysis of neuronal activity is studied by the example of the Hindmarsh-Rose (HR) model. For the parametric region of tonic spiking oscillations, it is shown that random noise transforms the spiking dynamic regime into the bursting one. This stochastic phenomenon is specified by qualitative changes in distributions of random trajectories and interspike intervals (ISIs). For a quantitative analysis of the noise-induced bursting, we suggest a constructive semi-analytical approach based on the stochastic sensitivity function (SSF) technique and the method of confidence domains that allows us to describe geometrically a distribution of random states around the deterministic attractors. Using this approach, we develop a new algorithm for estimation of critical values for the noise intensity corresponding to the qualitative changes in stochastic dynamics. We show that the obtained estimations are in good agreement with the numerical results. An interplay between noise-induced bursting and transitions from order to chaos is discussed. © 2018 World Scientific Publishing Company.The work was supported by Russian Science Foundation (N 16-11-10098)

Controlling the Stochastic Sensitivity in Nonlinear Discrete-Time Systems with Incomplete Information

For stochastic nonlinear discrete-time system with incomplete information, a problem of the stabilization of equilibrium is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations

Report / Institute für Physik

The 2017 Report of the Physics Institutes of the Universität Leipzig provides an overview of the structure and research activities of the three institutes. We are happy to announce that Prof. Dr. Caudia Schnohr from Universität Jena will join the Felix Bloch Institute for Solid State Physics beginning 2019 filling the vacant position in the department for Solid State Optics. Dr. Johannes Deiglmayr from ETH Zurich will establish an independent department for Quantum Optics at the same institute

Pseudoinversion Fractals

In this paper, we present some modifications of inversion fractals. The first modification is based on the use of different metrics in the inversion transformation. Moreover, we propose a switching process between different metric spaces. All the proposed modifications allowed us to obtain new and diverse fractal patterns that differ from the original inversion fractals