Nearly half a century ago, the German physicist Hermann Haken proved that laser dynamics could be described, under certain conditions, by Lorenz equations, paradigm of deterministic chaos. Unfortunately, its experimental realization has remained elusive for conventional materials and cavities mostly due to extreme pumping conditions low cavity quality factors (“bad-cavity condition”) required a...

In 1963, meteorologist Edward Lorenz suggested an approximate mathematical model (the Lorenz system) for the Rayleigh-Bénard convection and discovered numerically a chaotic attractor in this model [1]. This discovery stimulated rapid development of the chaos theory, numerical methods for attractor investigation, and till now has received a great deal of attention from different fields [2–7]. Th...

The nonlinear system of equations of relativistic Lorentz electrodynamics (LED) is studied in a “gyroscopic setup” in which the Lorentz electron is assumed to remain at rest, leaving the electromagnetic fields and the particle spin as the only dynamical degrees of freedom. The global existence and uniqueness of this gyroscopic spin-plus-field dynamics in unbounded space is proven. It is further...

Radar waveforms based on chaotic systems have occasionally been suggested for a variety of radar applications. In this paper, radar waveforms are constructed with solutions from a particular chaotic system, the Lorenz system, and are called Lorenz waveforms. Waveform properties, which include the peak autocorrelation function side-lobe and the transmit power level, are related to the system par...

Abstract Correction of Lorentz dispersion relation can be carried out through invariance violation (LIV). In the curved space-time with general stationary black holes, fermions dynamic equations have been modified more accurately according to Lorenz relation, and solved obtain a new expression quantum tunneling rate, hole Hawking temperature, entropy, other physical quantities holes. These expr...

In this paper, a system of Lorenz-type ordinary differential equations is considered and, under some assumptions about the parameter space, presence supercritical non-degenerate Hopf bifurcation demonstrated. The technical tool used consists Central Manifold theorem, well-known formula to calculate Lyapunov coefficient and Hopf’s Theorem. For particular values parameters in space established ma...

Ranking Intersecting Lorenz Curves This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations two alternative sequences of nested dominance criteria between Lorenz curves are introduced. At ...