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We study the dynamics of the periodically-forced May-Leonard system. We extend previous results on the field and we identify different dynamical regimes depending on the strength of attraction $delta$ of the network and the frequency $omega$ of the periodic forcing. We focus our attention in the case $deltagg1$ and $omega approx 0$, where we show that, for a positive Lebesgue measure set of parameters (amplitude of the periodic forcing), the dynamics are dominated by strange attractors with fully stochastic properties, supporting a Sinai-Ruelle-Bowen (SRB) measure. The proof is performed by using the Wang and Young Theory of rank-one strange attractors. This work ends the discussion about the existence of observable and sustainable chaos in this scenario. We also identify some bifurcations occurring in the transition from an attracting two-torus to rank-one strange attractors, whose existence has been suggested by numerical simulations.
In this paper we investigate how many periodic attractors maps in a small neighbourhood of a given map can have. For this purpose we develop new tools which help to make uniform cross-ratio distortion estimates in a neighbourhood of a map with degenerate critical points.
This paper shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible dynamical system
We analyse a periodically-forced SIR model to investigate the influence of seasonality on the disease dynamics and we show that the condition on the basic reproduction number $mathcal{R}_0<1$ is not enough to guarantee the elimination of the disease.
In this article we construct the parameter region where the existence of a homoclinic orbit to a zero equilibrium state of saddle type in the Lorenz-like system will be analytically proved in the case of a nonnegative saddle value. Then, for a qualit
There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attracting robust heteroclinic network defined on the two-sphere. We derive