Minimal Universal Model for Chaos in Laser with Feedback

We revisit the model of the laser with feedback and the minimal nonlinearity leading to chaos. Although the model has its origin in laser physics, with peculiarities related to the [Formula: see text] laser, it belongs to the class of the three-dimensional paradigmatic nonlinear oscillator models giving chaos. The proposed model contains three key nonlinearities, two of which are of the type [Formula: see text], where [Formula: see text] and [Formula: see text] are the fast and slow variables. The third one is of the type [Formula: see text], where [Formula: see text] is an intermediate feedback variable. We analytically demonstrate that it is essential for producing chaos via local or global homoclinic bifurcations. Its electronic implementation in the range of kilo Hertz region confirms its potential in describing phenomena evolving on different time scales.

Dynamics of a plant-herbivore model with a chemically-mediated numerical response

A system of two ordinary differential equations is proposed to model chemically-mediated interactions between plants and herbivores by incorporating a toxin-modifiednumerical response. This numerical response accounts for the reduction in the her-bivore's growth and reproduction due to chemical defenses from plants. It is shownthat the system exhibits very rich dynamics including saddle-node bifurcations, Hopfbifurcations, homoclinic bifurcations and co-dimension 2 bifurcations. Numerical sim-ulations are presented to illustrate the occurrence of multitype bistability, limit cycles,homoclinic orbits and heteroclinic orbits. We also discuss the ecological implicationsof the resulting dynamics.

Homoclinic Bifurcations and Chaos in the Fishing Principle for the Lorenz-like Systems

In this article using an analytical method called Fishing principle we obtain the region of parameters, where the existence of a homoclinic orbit to a zero saddle equilibrium in the Lorenz-like system is proved. For a qualitative description of the different types of homoclinic bifurcations, a numerical analysis of the obtained region of parameters is organized, which leads to the discovery of new bifurcation scenarios.

A Route to Chaos in the Boros–Moll Map

The Boros–Moll map appears as a subsystem of a Landen transformation associated to certain rational integrals and its dynamics is related to their convergence. In the paper, we study the dynamics of a one-parameter family of maps which unfold the Boros–Moll one, showing that the existence of an unbounded invariant chaotic region in the Boros–Moll map is a peculiar feature within the family. We relate this singularity with a specific property of the critical lines that occurs only for this special case. In particular, we explain how the unbounded chaotic region in the Boros–Moll map appears. We especially explain the main contact/homoclinic bifurcations that occur in the family. We also report some other bifurcation phenomena that appear in the considered unfolding.