We report a systematic two-parameter study of the organization mixed-mode oscillations and period-adding sequences observed in an extended Bonhoeffer–van der Pol FitzHugh–Nagumo oscillator. For both systems, we construct isospike diagrams show that number spikes their periodic are organized remarkable hierarchical way, forming Stern–Brocot tree. The tree is more general than Farey conjecture to also underlie structure other systems supporting oscillations.

We investigate the distribution of mixed-mode oscillations in control parameter space for two paradigmatic chemical models: a three-variable fourteen-parameter model Belousov-Zhabotinsky reaction and four-parameter autocatalator. For both systems, several high-resolution phase diagrams show that number spikes their emerges consistently organized surprising unexpected symmetrical way, forming Stern-Brocot trees. The tree is more general contains Farey as subtree. conjecture hierarchical...

Abstract. Cellular automata have been successfully applied to simulate the propagation of wildfires with aim assisting fire managers in defining suppression tactics and planning risk management policies. We present a cellular automaton designed severe wildfire episode that took place Algarve (southern Portugal) July 2012. During almost 25 000 ha burned there was an explosive stage between 33 h after onset. Results obtained show is adequately modeled when introducing wind rule which allowed...

We report a detailed numerical investigation of the relative abundance periodic and chaotic oscillations in phase diagrams for Belousov–Zhabotinsky (BZ) reaction as described by nonpolynomial, autonomous, three-variable model suggested Györgyi Field [Nature (London) 355, 808 (1992)]. The contains 14 parameters that may be tuned to produce rich dynamical scenarios. By computing Lyapunov spectra, we find structuring phases BZ display unusual global patterns, very distinct from those recently...

Incomplete homoclinic scenarios were recently measured in a semiconductor laser with optoelectronic feedback. We show here that such contains cascades of spirals periodic oscillations and hubs which look identical to the familiar ones observed complete scenarios. This means are far more general than presumed so far, being not limited by Shilnikov's theorem. Laser open possibility measuring complex distributions non-Shilnikov oscillations, we briefly discuss how do it.

We report the experimental discovery of a remarkable organization set self-generated periodic oscillations in parameter space nonlinear electronic circuit. When control parameters are suitably tuned, wave pattern complexity is found to increase orderly without bound. Such complex patterns emerge forming self-similar discontinuous phases that combine an artful way produce large spirals stability. This unanticipated discrete accumulation stability was detected experimentally and numerically...

We report the discovery of a regular lattice exceptional quint points in periodically driven oscillator, namely, frequency–amplitude control parameter space photochemically perturbed ruthenium-catalyzed Belousov–Zhabotinsky reaction model. Quint are singular boundary where five distinct stable oscillatory phases coalesce. While spikes activator show smooth and continuous variation, inhibitor an intricate but branching into myriad that have fivefold contact points. Such form wide as function...

We report a detailed experimental study of the complex behavior dc low-pressure plasma discharge tube type commonly used in commercial illuminated signs, microfluidic chip recently proposed for visible analog computing, and other practical devices. Our experiments reveal clear quasiperiodicity route to chaos, two competing frequencies being relaxation frequency eigenfrequency. Based on an volt-ampere characterization discharge, we propose macroscopic model current flowing plasma. The model,...

We study the global organization of oscillations in sigmoidal maps, a class models which reproduces complex locking behaviors commonly observed lasers, neurons, and other systems display spiking, bursting, chaotic sequences spiking bursting. find periodic to emerge organized regularly according elusive Stern-Brocot tree, symmetric more general tree contains better-known asymmetric Farey as sub-tree. The provides natural encompassing classify nonlinear oscillations. mathematical algorithm for...

Recently, an electro-kinetic model based on a specified reaction scheme for the electro-oxidation of formic acid platinum was reported. The evaluated three pathways towards production CO2: dehydrogenation and dehydration acid, third most active pathway includes fast oxidation formate ion. Numerical integrations showed that is well-suited to describe experimental results in voltammetric oscillatory regimes. In present paper, we provide detailed stability phase diagrams characterizing...

We report phase diagrams detailing the intransitivity observed in climate scenarios supported by a prototype atmospheric general circulation model, namely, Lorenz-84 low-order model. So far, this model was known to have pair of coexisting climates described originally Lorenz. Bifurcation analysis allows identification remarkably wide parameter region where up four coexist simultaneously. In dynamical behavior depends crucially on subtle and minute tuning parameters. This strong sensitivity...

The investigation of regular and irregular patterns in nonlinear oscillators is an outstanding problem physics all natural sciences. In general, regularity understood as tantamount to periodicity. However, there now a flurry works proving the existence “antiperiodicity”, unfamiliar type regularity. Here we report experimental observation numerical corroboration antiperiodic oscillations. contrast isolated solutions presently known, infinite hierarchies waveforms that can be tuned...

We report a detailed investigation of the stability CO2 laser with feedback as described by six-dimensional rate-equations model which provides satisfactory agreement between numerical and experimental results. focus on experimentally accessible parameters, like bias voltage, gain, bandwidth loop. The impact decay rates parameters controlling cavity losses are also investigated well control planes imply changes physical medium. For several parameter combinations, we diagrams detailing how...

Abstract Background Staphylococcus aureus is one of the leading causes bloodstream infections (BSI) worldwide. In Brazil, hospital-acquired methicillin-resistant S. USA100/SCC mec II lineage replaced previously well-established clones. However, emergence community-associated (CA) MRSA lineages among hospitalized patients an increasing issue. Methods Consecutive isolates recovered from BSI episodes admitted between January 2016 and December 2018 in a Brazilian teaching hospital were tested...

The impact of predator dormancy on the population dynamics phytoplankton-zooplankton in freshwater ecosystems is investigated using a simple model including dormancy, strategy to avoid extinction. In addition recently reported chaos-mediated mixed-mode oscillations, as carrying capacity grows, we find surprisingly wide phases nonchaos-mediated oscillations be present well before onset chaos system. Nonchaos-mediated cascades display spike-adding sequences, while show spike-doubling. A host...

We report a startling mosaic-like organization of stability phases found in the low-frequency limit driven Brusselator. Such correspond to periodic oscillations having constant number spikes per period. The mosaic is free from chaotic and formed by an apparently infinite cascade whose grow without bound. Wide windows chaos but supporting unbounded quantities complex are potentially interest operate oscillators such as lasers, electronic circuits, biochemical pacemakers.

Oscillators have widespread applications in micro- and nanomechanical devices, lasers of various types, chemical biochemical models, among others. However, are normally marred by the presence chaos, requiring expensive control techniques to bypass it. Here, we show that low-frequency limit driven systems, a poorly explored region, is wide chaos-free zone. Specifically, for popular model devices Brusselator, report discovery an unexpectedly mosaic phases resulting from stable periodic...

We study the dynamics of patterns exhibited by rule 52, a totalistic cellular automaton displaying intricate behaviors and wide regions active/inactive synchronization patches. Systematic computer simulations involving 2(30) initial configurations reveal that all complexity in this originates from random juxtaposition very small number interfaces delimiting Such are studied with sidewise spatial updating algorithm. This novel tool allows us to prove found empirically only possible for these...