Olga A. Kuznetsova

Analytical-Numerical Localization of Hidden Attractor in Electrical Chua’s Circuit

Study of hidden oscillations and hidden chaotic attractors (basin of attraction of which does not contain neighborhoods of equilibria) requires the development of special analytical-numerical methods. Development and application of such methods for localization of hidden chaotic attractors in dynamical model of Chua’s circuit are demonstrated in this work.

Limitations of the classical phase-locked loop analysis

Nonlinear analysis of the classical phase-locked loop (PLL) is a challenging task. In classical engineering literature simplified mathematical models and simulation are widely used for its study. In this work the limitations of classical engineering phase-locked loop analysis are demonstrated, e.g., hidden oscillations, which can not be found by simulation, are discussed. It is shown that the use of simplified mathematical models and the application of simulation may lead to wrong conclusions concerning the operability of PLL-based circuits.

A short survey on nonlinear models of the classic Costas loop: Rigorous derivation and limitations of the classic analysis

Rigorous nonlinear analysis of the physical model of Costas loop-a classic phase-locked loop (PLL) based circuit for carrier recovery, is a challenging task. Thus for its analysis, simplified mathematical models and numerical simulation are widely used. In this work a short survey on nonlinear models of the BPSK Costas loop, used for pre-design and post-design analysis, is presented. Their rigorous derivation and limitations of classic analysis are discussed. It is shown that the use of simplified mathematical models, and the application of non rigorous methods of analysis (e.g., simulation and linearization) may lead to wrong conclusions concerning the performance of the Costas loop physical model.

Simulation of nonlinear models of QPSK costas loop in MatLab Simulink

Nowadays simplified mathematical models and numerical simulation are widely used for the analysis of QPSK Costas loop. In the work it is shown that the use of simplified mathematical models and the application of non-rigorous methods of analysis may lead to wrong conclusions concerning the operability of real model of QPSK Costas loop.

BPSK Costas loop: Simulation of nonlinear models in MatLab Simulink

Nonlinear analysis of BPSK Costas loop is a difficult task, so for its analysis simplified mathematical models and their simulation are widely used. In the work it is shown that the use of simplified mathematical models and the application of non-rigorous methods of analysis may lead to wrong conclusions concerning the operability of real model of BPSK Costas loop. Corresponding examples of BPSK Costas loop simulation in MatLab Simulink are presented.

Hidden and self-excited attractors in Chua circuit: synchronization and SPICE simulation

Graphical Abstract Two symmetric hidden chaotic attractors (blue), trajectories (red) from unstable manifolds of two saddle points are either attracted to locally stable zero equilibrium, or tend to infinity; trajectories (black) from stable manifolds tend to equilibria. Abstract Nowadays various chaotic secure communication systems based on synchronization of chaotic circuits are widely studied. To achieve synchronization, the control signal proportional to the difference between the circuits signals, adjust the state of one circuit. In this paper the synchronization of two Chua circuits is simulated in Simulation Programs with Integrated Circuit Emphasis. It is shown that the choice of control signal is not straightforward, especially in the case of multistability and hidden attractors.

Nonlinear models of BPSK Costas loop

Rigorous nonlinear analysis of the physical model of Costas loop is very difficult task, so for analysis, simplified mathematical models and numerical simulation are widely used. In the work it is shown that the use of simplified mathematical models, and the application of non rigorous methods of analysis may lead to wrong conclusions concerning the operability of Costas loop.

Switching algorithm for data fusion of small low-cost UAV navigation system

Abstract The switching algorithm for fusion data of satellite navigation system and standard onboard sensors for low-cost unmanned aerial vehicle (UAV) is proposed and numerically studied by the example of the hypothetical small jet-propelled UAV.