Coexisting Attractors in a Heterogeneous Agent Model in Discrete Time

Coexisting Attractors and Complex Basins in Discrete-time Economic Models

In this lesson we consider discrete time dynamical systems with coexisting attractors, and we analyze the problem of the structure of the boundaries that separate their basins of attraction. This problem may become particularly challenging when the discrete dynamical system is represented by the iteration of a noninvertible map, because in this case nonconnected basins can be obtained, formed b...

Dynamics of a discrete-time plant-herbivore model

Intermittent control of coexisting attractors.

This paper proposes a new control method applicable for a class of non-autonomous dynamical systems that naturally exhibit coexisting attractors. The central idea is based on knowledge of a system's basins of attraction, with control actions being applied intermittently in the time domain when the actual trajectory satisfies a proximity constraint with regards to the desired trajectory. This in...

Coexisting Hidden Attractors in a 4-D Simplified Lorenz System

A new simple four-dimensional equilibrium-free autonomous ODE system is described. The system has seven terms, two quadratic nonlinearities, and only two parameters. Its Jacobian matrix everywhere has rank less than 4. It is hyperchaotic in some regions of parameter space, while in other regions it has an attracting torus that coexists with either a symmetric pair of strange attractors or with ...

Coexisting chaotic climate attractors in a two-layer quasi-geostrophic model

An intriguing manifestation of the underlying nonlinear fluid dynamic character of the atmosphere is found in a simple quasi-geostrophic model of the troposphere. For identical forcing and dissipation, the model’s climate is found to depend sensitively upon the choice of initial conditions, tending either toward a state resembling the current Northern Hemisphere wintertime circulation, characte...