One-Dimensional Ferronematics in a Channel: Order Reconstruction, Bifurcations, and Multistability

Adaptive decision dynamics: Bifurcations, multistability and chaos

In this paper we propose a model describing the dynamical process of decision and opinion formation of two economic homogeneous interacting and boundedly rational agents. The decisional process represented in our model is given by an adaptive adjustment mechanism in which two agents take into account the difference between their own opinion and the opinion of the other agent. The smaller that d...

Multistability and nonsmooth bifurcations in the Quasiperiodically forced Circle Map

It is well-known that the dynamics of the Arnold circle map is phase-locked in regions of the parameter space called Arnold tongues. If the map is invertible, the only possible dynamics is either quasiperiodic motion, or phase-locked behavior with a unique attracting periodic orbit. Under the influence of quasiperiodic forcing the dynamics of the map changes dramatically. Inside the Arnold tong...

Border collision bifurcations in one-dimensional linear-hyperbolic maps

In this paper we consider a continuous one-dimensional map, which is linear on one side of a generic kink point and hyperbolic on the other side. This kind of map is widely used in the applied context. Due to the simple expression of the two functions involved, in particular cases it is possible to determine analytically the border collision bifurcation curves that characterize the dynamic beha...

Bifurcations of Chaotic Attractors in One-Dimensional Piecewise Smooth Maps

It is well known that dynamical systems defined by piecewise smooth functions exhibit several phenomena which cannot occur in smooth systems, such as for example, border collision bifurcations, sliding, chattering, etc. [di Bernardo et al., 2008]. One such phenomenon is the persistence of chaotic attractors under parameter perturbations, referred to as robust chaos [Banerjee et al., 1998]. In t...

One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures.