We investigate the bifurcation mechanism for the loss of transverse stability of the chaotic attractor in an invariant subspace in an asymmetric dynamical system. It is found that a direct transition to global riddling occurs through a transcritical contact bifurcation between a periodic saddle embedded in the chaotic attractor on the invariant subspace and a repeller on its basin boundary. Thi...

We explore the multifractal, self-similar organization of heteroclinic and homoclinic bifurcations of saddle singularities in the parameter space of the Shimizu–Morioka model that exhibits the Lorenz chaotic attractor. We show that complex transformations that underlie the transitions from the Lorenz attractor to wildly chaotic dynamics are intensified by Shilnikov saddle-foci. These transforma...

In our previous paper, it was confirmed that the unstable periodic orbit embedded in the chaotic attractor in magneto-elastic beam system can be stabilized by delayed feedback control experimentally. It seems an advantage that the control method does not require any exact model of the system. However, the application of the control raises the problem that we cannot predict the stabilized unstab...

We describe a method for introducing variations into predeened dance sequences using a chaotic mapping. A symbol sequence representing a dance piece is mapped onto a chaotic trajectory, establishing a symbolic dynamics that links the dance sequence and the attractor structure. A choreographic variation on the original piece is created by generating a trajectory with slightly diierent initial co...

There are many examples of nonconnected chaotic attractors consisting of several components. The determination of an overall period of such a system is typically done only by a numerical integration of the system. In this letter, we provide a rigorous proof that the exact value of the overall period of a particular 2-D chaotic attractor from an iterated map is two once the attractor has been pa...

The "tea-cup" attractor of a classical prey-predator-superpredator food chain model is studied analytically. Under the assumption that each species has its own time scale, ranging from fast for the prey to intermediate for the predator and to slow for the superpredator, the model is transformed into a singular perturbed system. It is demonstrated that the singular limit of the attractor contain...

A simple and transparent example of a non-autonomous flow system, with hyper-bolic strange attractor is suggested. The system is constructed on a basis of two coupled van der Pol oscillators, the characteristic frequencies differ twice, and the parameters controlling generation in both oscillators undergo a slow periodic counter-phase variation in time. In terms of stroboscopic Poincaré section...

A system of non-linear di€erence equations is used to model the e€ects of density-dependent selection and migration in a population characterized by two alleles at a single gene locus. Results for the existence and stability of polymorphic equilibria are established. Properties for a genetically important class of equilibria associated with complete dominance in ®tness are described. The birth ...

This paper presents an analysis of the nonlinear dynamics of a Charge Pump Phase-Locked Loop. The closed-loop circuit is modelled using decision-based equations developed by Van Paemel. State space plots; bifurcation diagrams and the presence of a chaotic attractor all indicate a significant level of underlying nonlinear phenomena. A calculation of the fractal dimension of the chaotic attractor...

Running title: Analysis of a discrete one-island migration model Abstract. A system of nonlinear diierence equations is used to model the eeects of density-dependent selection and migration in a population characterized by two alleles at a single gene locus. Results for the existence and stability of polymorphic equilibria are established. Properties for a genetically important class of equilib...