Hidden hyperchaos and electronic circuit application in a 5D self-exciting homopolar disc dynamo
We report on the finding of hidden hyperchaos in a 5D extension to a known 3D self-exciting
homopolar disc dynamo. The hidden hyperchaos is identified through three positive …
homopolar disc dynamo. The hidden hyperchaos is identified through three positive …
Phase slips in coupled oscillator systems
Phase slips are a typical dynamical behavior in coupled oscillator systems: the route to
phase synchrony is characterized by intervals of constant phase difference interrupted by …
phase synchrony is characterized by intervals of constant phase difference interrupted by …
A new class of two-dimensional chaotic maps with closed curve fixed points
This paper constructs a new class of two-dimensional maps with closed curve fixed points.
Firstly, the mathematical model of these maps is formulated by introducing a nonlinear …
Firstly, the mathematical model of these maps is formulated by introducing a nonlinear …
Forecasting and stabilizing chaotic regimes in two macroeconomic models via artificial intelligence technologies and control methods
One of the key tasks in the economy is forecasting the economic agents' expectations of the
future values of economic variables using mathematical models. The behavior of …
future values of economic variables using mathematical models. The behavior of …
Perpetual points: new tool for localization of coexisting attractors in dynamical systems
Perpetual points (PPs) are special critical points for which the magnitude of acceleration
describing the dynamics drops to zero, while the motion is still possible (stationary points are …
describing the dynamics drops to zero, while the motion is still possible (stationary points are …
Augmented Perpetual Manifolds and Perpetual Mechanical Systems—Part I: Definitions, Theorem, and Corollary for Triggering Perpetual Manifolds, Application in …
F Georgiades - Journal of Computational and …, 2021 - asmedigitalcollection.asme.org
Perpetual points in mechanical systems were defined recently. Herein, they are used to seek
specific solutions of N-degrees-of-freedom systems, and their significance in mechanics is …
specific solutions of N-degrees-of-freedom systems, and their significance in mechanics is …
Augmented perpetual manifolds, a corollary: dynamics of natural mechanical systems with eliminated internal forces
F Georgiades - Advances in Nonlinear Dynamics: Proceedings of the …, 2022 - Springer
Perpetual points have been defined, in mathematics, recently, and their role in the dynamics
of systems is on-going research. In unforced linear and some nonlinear mechanical …
of systems is on-going research. In unforced linear and some nonlinear mechanical …
Describing chaotic attractors: Regular and perpetual points
We study the concepts of regular and perpetual points for describing the behavior of chaotic
attractors in dynamical systems. The idea of these points, which have been recently …
attractors in dynamical systems. The idea of these points, which have been recently …
Controlling hidden dynamics and multistability of a class of two-dimensional maps via linear augmentation
This paper reports the complex dynamics of a class of two-dimensional maps containing
hidden attractors via linear augmentation. Firstly, the method of linear augmentation for …
hidden attractors via linear augmentation. Firstly, the method of linear augmentation for …
A class of two-dimensional rational maps with self-excited and hidden attractors
This paper studies a new class of two-dimensional rational maps exhibiting self-excited and
hidden attractors. The mathematical model of these maps is firstly formulated by introducing …
hidden attractors. The mathematical model of these maps is firstly formulated by introducing …