Canards are solutions of slow-fast systems that spend long times near branches of repelling equilibria, periodic orbits, or higher-dimensional invariant sets. Here, we report on the observation of a new type of canard orbit, labeled a canard of mixed type. This canard orbit is a hybrid of the classical limit cycle canards, which spend long times near attracting and repelling branches of equilib...

Three bodies moving in a periodic orbit under the influence of Newtonian gravity ought to emit gravitational waves. We have calculated the gravitational radiation quadrupolar waveforms and the corresponding luminosities for the 13+11 recently discovered three-body periodic orbits in Newtonian gravity. These waves clearly allow one to distinguish between their sources: all 13+11 orbits have diff...

We discuss dynamics near homoclinic orbits to saddle-focus equilibria in threedimensional vector fields. The existence of periodic and strange attractors is investigated not in unfoldings, but in families for which each member has a homoclinic orbit. We consider how often, in the sense of measure, periodic and strange attractors occur in such families. We also discuss the fate of typical orbits...

In this paper a new design for controlling dynamical systems has been applied to buck converters driven with a PWM centered pulse and (Zero Average Dynamics) ZAD-strategy. Chaotic operation has been stabilized with the so-called Fixed Point Induced Control (FPIC) technique. Also, the same converter with delay, whose 1-periodic orbit is always unstable, has been stabilized. Simulations are compa...

For finite-dimensional maps and periodic systems, Palmer rigorously proved Smale horseshoe theorem using shadowing lemma in 1988 [20]. For infinitedimensional maps and periodic systems, such a proof was completed by Steinlein and Walther in 1990 [30], and Henry in 1994 [9]. For finite-dimensional autonomous systems, such a proof was accomplished by Palmer in 1996 [17]. For infinite-dimensional ...

A simple reversible Turing machine with four states, three symbols and no halting configuration is constructed that has no periodic orbit, simplifying a construction by Blondel, Cassaigne and Nichitiu and positively answering a conjecture by Kari and Ollinger. The constructed machine has other interesting properties: it is symmetric both for space and time and has a topologically minimal associ...

We report experimental control of chaos in an electronic circuit at 43.9 MHz, which is the fastest chaos control reported in the literature to date. Limiter control is used to stabilize a periodic orbit in a tuned collector transistor oscillator modified to exhibit simply folded band chaos. The limiter is implemented using a transistor to enable monitoring the relative magnitude of the control ...

Conditions under which a single oscillator model coupled with Dieterich-Ruina’s rate and state dependent friction exhibits chaotic dynamics is studied. Properties of spring-block models are discussed. The parameter values of the system are explored and the corresponding numerical solutions presented. Bifurcation analysis is performed to determine the bifurcations and stability of stationary sol...

A class of autocatalytic reaction networks based on template-dependent replication and specific catalysis is considered. Trimolecular "elementary steps" of simple replicator dynamics are resolved into two consecutive irreversible reactions. The extreme cases, competition for common resources and hypercycle-like cooperative feedback, were analyzed in some detail. Although the dynamics of the ext...

We discuss the number variance 2 (L) and the spectral form factor F() of the energy levels of bound quantum systems whose classical counterparts are strongly chaotic. Exact periodic{orbit representations of 2 (L) and F() are derived which explain the breakdown of universality, i. e., the deviations from the predictions of random{matrix theory. The relation of the exact spectral form factor F() ...