Research in multistable systems is a flourishing field with countless examples and applications across scientific disciplines. I present a catalog of multistable dynamical systems covering relevant fields of knowledge. This work is focused on providing a research tool to the community in the form classified examples and computer code to reproduce basins of attraction. The companion code to this article can be found at https://github.com/awage/BasinsCollection or https://doi.org/10.5281/zenodo.15124200.
We will study the relationship between two well-known theories, genetic evolution and random matrix theory in the context of many-body systems. It is suggested that genetic evolution can be described by a random matrix theory with statistical distribution in which mutation acts as a Gross-Witten-Wadia phase transition.
We consider the concept of statistical complexity to write the quasiperiodical damped systems applying the snapshot attractors. This allows us to understand the behaviour of these dynamical systems by the probability distribution of the time series making a difference between the regular, random and structural complexity on finite measurements. We interpreted the statistical complexity on snapshot attractor and determined it on the quasiperiodical forced pendulum.
The paper introduces a new 4d dynamical system leading to a typical 4d strange attractor. Its focal statement appears in its total disconnection from previous 3D nonlinear systems.
We elucidate conditions for chaos anti-synchronization between two uni-directionally coupled multiple time delay power systems. The results are of some importance to prevent power black-out in the entire power grid.
The letter by Mark Perakh entitled "DEFINING COMPLEXITY: A Commentary to a paper by Charles H. Bennett" is here archived with the permission of the author. This letter was downloaded from the site "On Talk Reason, http://www.talkreason.org/articles/complexity.pdf, August (2004)".
Intermittent high-amplitude structures emerge in a damped and driven discrete nonlinear Schroedinger equation whose solutions transport both energy and particles from sources to sinks. These coherent structures are necessary for any solution that has statistically stationary transport properties.
The statistics of S-matrix fluctuations are numerically investigated on a model for irregular quantum scattering in which a classical chaotic diffusion takes place within the interaction region. Agreement with various random-matrix theoretic predictions is discussed in the various regimes (ballistic, diffusive, localized).
A phenomenological model for the inertial range scaling of passive-scalar turbulence is developed based on a bivariate log-Poisson model. An analytical formula of the scaling exponent for three-dimensional passive-scalar turbulence is deduced. The predicted scaling exponents are compared with experimental measurements, showing good agreement.
The three-dimensional stability problem of a stretched stationary vortex is addressed in this letter. More specifically, we prove that the discrete part of the temporal spectrum is only associated with two-dimensional perturbations.
We show that Lyapunov exponent for the Sinai billiard is $λ= -2\log(R)+C+O(R\log^2 R)$ with $C=1-4\log 2+27/(2π^2)\cdot ζ(3)$ where $R$ is the radius of the circular scatterer. We consider the disk-to-disk-map of the standard configuration where the disks is centered inside a unit square.
For a short-correlated Gaussian velocity field the problem of a passive scalar with the imposed constant gradient is considered. It is shown that the scaling of three-point correlation function is anomalous. In the limit of large dimension of space $d$ anomalous exponent is calculated.
We establish sufficient conditions for the hyperbolicity of the billiard dynamics on surfaces of constant curvature. This extends known results for planar billiards. Using these conditions, we construct large classes of billiard tables with positive Lyapunov exponents on the sphere and on the hyperbolic plane.
In this paper we investigate dual synchronization and dual-cross synchronization between the transmitter and receiver, each one consisting of two master and slave systems. These findings are considered to be of interest in multichannel communication schemes.
This is the transcript of a lecture given at UMass-Lowell in which I compare and contrast the work of Godel and of Turing and my own work on incompleteness. I also discuss randomness in physics vs randomness in pure mathematics.