After the discovery in early 1960s by E. Lorenz and Y. Ueda of the first example of a chaotic
attractor in numerical simulation of a real physical process, a new scientific direction of …

The development of the theory of absolute stability, the theory of bifurcations, the theory of
chaos, theory of robust control, and new computing technologies has made it possible to …

On the example of the famous Lorenz system, the difficulties and opportunities of reliable
numerical analysis of chaotic dynamical systems are discussed in this article. For the Lorenz …

Chaos theory for three-dimensional autonomous systems has been intensively and
extensively studied since the time of Edward N. Lorenz in the 1960s, and the theory has …

Phase-locked loops (PLLs) are nonlinear automatic control circuits widely used in
telecommunications, computer architecture, gyroscopes, and other applications. One of the …

Within the framework of the development of the theory of hidden oscillations, the problem of
determining the boundary of global stability and revealing its hidden parts corresponding to …

In 1981, famous engineer William F. Egan conjectured that a higher-order type 2 PLL with
an infinite hold-in range also has an infinite pull-in range, and supported his conjecture with …

In this paper a fairly complete mathematical model of CP-PLL, which reliable enough to
serve as a tool for credible analysis of dynamical properties of these circuits, is studied. We …

In the present work, a second-order type-2 phase-locked loop (PLL) with a piecewise-linear
phase detector characteristic is analyzed. An exact solution to the Gardner problem on the …

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