相关论文: Structure analysis of the Lorenz-84 chaotic attrac…
Theoretical foundations of chaos have have been predominantly laid out for finite-dimensional dynamical systems, such as the three-body problem in classical mechanics and the Lorenz model in dissipative systems. In contrast, many real-world…
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…
For systems with hidden attractors and unstable equilibria, the property that hidden attractors are not connected with unstable equilibria is now accepted as one of their main characteristics. To the best of our knowledge this property has…
Morphogenesis, as it is understood in a wide sense by Ren\'e Thom, is considered for various types of chaos. That is, those, obtained by period-doubling cascade, Devaney's and Li-Yorke chaos. Moreover, in discussion form we consider…
The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…
The well known butterfly effect got its nomenclature from its two wings geometrical structure in phase space. There are chaotic dynamics from simple one-wing to multiple-wings complex structures in phase space. In this communication we…
We recently described a specific type of attractors of two-dimensional discontinuous piecewise linear maps, characterized by two discontinuity lines dividing the phase plane into three partitions, related to economic applications. To our…
We consider a system of two identical linearly coupled Lorenz oscillators, presenting synchro- nization of chaotic motion for a specified range of the coupling strength. We verify the existence of global synchronization and…
We present a method for generating robust chaos. It is based on the search algorithm weak symmetry violation in the reconstructed attractor. On its basis the smooth functions in the form of a system of finite-difference equations. To ensure…
We consider the unsteady regimes of an acoustically-driven jet that forces a recirculating flow through successive reflections on the walls of a square cavity. The specific question being addressed is to know whether the system can sustain…
We explore the dynamical and topological characteristics of the R\"ossler system that lead to the existence of a periodicity hub and nested spiral in codimension-2 parameter space. We find that the hub shape is a consequence of conjugacy…
The harmonic oscillator is an essential tool, widely used in all branches of Physics in order to understand more realistic systems, from classical to quantum and relativistic regimes. We know that the harmonic oscillator is integrable in…
We present new results of numerical simulations for driven vortex lattices in presence of random disorder at zero temperature. We show that the plastic dynamics of vortices display dissipative chaos. Intermittency "routes to chaos" have…
Following the Nambu mechanics framework we demonstrate that the non-dissipative part of the Lorenz system can be generated by the intersection of two quadratic surfaces that form a doublet under the group SL(2,R). All manifolds are…
We report in this paper a complete analytical study on the bifurcations and chaotic phenomena observed in certain second-order, non-autonomous, dissipative chaotic systems. One-parameter bifurcation diagrams obtained from the analytical…
The collection of all non-degenerate, continuous, two-piece, piecewise-linear maps on $\mathbb{R}^2$ can be reduced to a four-parameter family known as the two-dimensional border-collision normal form. We prove that throughout an open…
Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…
We study the bifurcation diagram of the R\"ossler system. It displays the various dynamical regimes of the system (stable or chaotic) when a parameter is varied. We choose a diagram that exhibits coexisting attractors and banded chaos. We…
We consider a certain three-dimensional piecewise linear system of Lorenz type in the cases of positive and negative saddle value, which is the sum of two eigenvalues of the saddle nearest to zero. This system was recently proposed and…
We analyze the origin and properties of the chaotic dynamics of two atomic ensembles in a driven-dissipative experimental setup, where they are collectively damped by a bad cavity mode and incoherently pumped by a Raman laser. Starting from…