Related papers: Basins of attraction of a nonlinear nanomechanical…
In this paper we consider the problem of reconstructing separatrices in dynamical systems. In particular, here we aim at partitioning the domain approximating the boundaries of the basins of attraction of different stable equilibria. We…
The present paper investigates the binary system of quasars in the framework of the Circular Restricted Three-Body Problem. The parametric evolution of libration points, the geometry of zero-velocity curves are one of the crucial aspects of…
We consider dissipative periodically forced systems and investigate cases in which having information as to how the system behaves for constant dissipation may be used when dissipation varies in time before settling at a constant final…
The Newton-Raphson basins of attraction, associated with the libration points (attractors), are revealed in the pseudo-Newtonian planar circular restricted three-body problem, where the primaries have equal masses. The parametric variation…
The basin of attraction is the set of initial points that will eventually converge to some attracting set. Its knowledge is important in understanding the dynamical behavior of a given dynamical system of interest. In this work, we address…
The Newton-Raphson basins of attraction, associated with the libration points (attractors), are revealed in the generalized Hill problem. The parametric variation of the position and the linear stability of the equilibrium points is…
The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two dimensional nonlinear mapping. When high dissipation is considered, the dynamics evolves to different attractors. The evolution of the…
We study a finite uni-directional array of "cascading" or "threshold coupled" chaotic maps. Such systems have been proposed for use in nonlinear computing and have been applied to classification problems in bioinformatics. We describe some…
In this paper, we investigate geometric properties of monotone systems by studying their isostables and basins of attraction. Isostables are boundaries of specific forward-invariant sets defined by the so-called Koopman operator, which…
In applied sciences, such as physics and biology, it is often required to model the evolution of populations via dynamical systems. In this paper, we focus on the problem of approximating the basins of attraction of such models in case of…
The range of existence and the properties of two essentially different chaotic attractors found in a model of nonlinear convection-driven dynamos in rotating spherical shells are investigated. A hysteretic transition between these…
Emergent bath-mediated attraction and condensation arise when multiple particles are simultaneously driven through an equilibrated bath under geometric constraints. While such scenarios are observed in a variety of non-equilibrium…
In this paper, we study geometric properties of basins of attraction of monotone systems. Our results are based on a combination of monotone systems theory and spectral operator theory. We exploit the framework of the Koopman operator,…
Using a system of two FitzHugh-Nagumo units, we demonstrate the occurrence of riddled basins of attraction in delay-coupled systems as the coupling between the units is increased. We characterize the riddled basin using the uncertainty…
We numerically explore the Newton-Raphson basins of convergence, related to the libration points (which act as attractors), in the planar circular restricted five-body problem (CR5BP). The evolution of the position and the linear stability…
Although neuron models have been well studied for their rich dynamics and biological properties, limited research has been done on the complex geometries that emerge from the basins of attraction and basin boundaries of multistable neuron…
We consider a pendulum with vertically oscillating support and time-dependent damping coefficient which varies until reaching a finite final value. The sizes of the corresponding basins of attraction are found to depend strongly on the full…
We report quantitative experimental measurements of the nonlinear response of a radiofrequency mechanical resonator, with very high quality factor, driven by a large swept-frequency force. We directly measure the noise-free transition…
The dynamics of the web map with weak linear dissipation is studied. The evolution of the coexisting attractors and the structure of their basins while changing the dissipation and nonlinearity are revealed. It is shown that the structure…
In dynamical systems saddle points partition the domain into basins of attractions of the remaining locally stable equilibria. This problem is rather common especially in population dynamics models. Precisely, a particular solution of a…