Analysis of noise-induced transitions from regular to chaotic oscillations in the Chen system

The stochastically perturbed Chen system is studied within the parameter region which permits both regular and chaotic oscillations. As noise intensity increases and passes some threshold value, noise-induced hopping between close portions of the stochastic cycle can be observed. Through these transitions, the stochastic cycle is deformed to be a stochastic attractor that looks like chaotic. In this paper for investigation of these transitions, a constructive method based on the stochastic sensitivity function technique with confidence ellipses is suggested and discussed in detail. Analyzing a mutual arrangement of these ellipses, we estimate the threshold noise intensity corresponding to chaotization of the stochastic attractor. Capabilities of this geometric method for detailed analysis of the noise-induced hopping which generates chaos are demonstrated on the stochastic Chen system. © 2012 American Institute of Physics

Chaotic versus stochastic behavior in active-dissipative nonlinear systems

We study the dynamical state of the one-dimensional noisy generalized Kuramoto-Sivashinsky (gKS) equation by making use of time-series techniques based on symbolic dynamics and complex networks. We focus on analyzing temporal signals of global measure in the spatiotemporal patterns as the dispersion parameter of the gKS equation and the strength of the noise are varied, observing that a rich variety of different regimes, from high-dimensional chaos to pure stochastic behavior, emerge. Permutation entropy, permutation spectrum, and network entropy allow us to fully classify the dynamical state exposed to additive noise

Steady-State L\'evy Flights in a Confined Domain

We derive the generalized Fokker-Planck equation associated with a Langevin equation driven by arbitrary additive white noise. We apply our result to study the distribution of symmetric and asymmetric L\'{e}vy flights in an infinitely deep potential well. The fractional Fokker-Planck equation for L\'{e}vy flights is derived and solved analytically in the steady state. It is shown that L\'{e}vy flights are distributed according to the beta distribution, whose probability density becomes singular at the boundaries of the well. The origin of the preferred concentration of flying objects near the boundaries in nonequilibrium systems is clarified.Comment: 10 pages, 1 figur

Noise-induced bistability in the quasi-neutral coexistence of viral RNAs under different replication modes

[EN] Evolutionary and dynamical investigations into real viral populations indicate that RNA replication can range between the two extremes represented by so-called 'stamping machine replication' (SMR) and 'geometric replication' (GR). The impact of asymmetries in replication for single-stranded (+) sense RNA viruses has been mainly studied with deterministic models. However, viral replication should be better described by including stochasticity, as the cell infection process is typically initiated with a very small number of RNA macromolecules, and thus largely influenced by intrinsic noise. Under appropriate conditions, deterministic theoretical descriptions of viral RNA replication predict a quasi-neutral coexistence scenario, with a line of fixed points involving different strands' equilibrium ratios depending on the initial conditions. Recent research into the quasi-neutral coexistence in two competing populations reveals that stochastic fluctuations fundamentally alter the mean-field scenario, and one of the two species outcompetes the other. In this article, we study this phenomenon for viral RNA replication modes by means of stochastic simulations and a diffusion approximation. Our results reveal that noise has a strong impact on the amplification of viral RNAs, also causing the emergence of noise-induced bistability. We provide analytical criteria for the dominance of (+) sense strands depending on the initial populations on the line of equilibria, which are in agreement with direct stochastic simulation results. The biological implications of this noise-driven mechanism are discussed within the framework of the evolutionary dynamics of RNA viruses with different modes of replication.The research leading to these results has received funding from 'la Caixa' Foundation. J.S. and T.A. have been partially funded by the CERCA Program of the Generalitat de Catalunya, MINECO grant no. MTM2015-71509-C2-1-R and by a MINECO grant awarded to the Barcelona Graduate School of Mathematics under the 'Maria de Maeztu' Program (grant no. MDM-2014-0445). T.A. is also supported by AGAUR (grant no. 2014SGR1307). S.F.E. has been supported by MINECO-FEDER grant no. BFU2015-65037-P and by Generalitat Valenciana grant no. PROMETEOII/2014/021.Sardanyes, J.; Arderiu, A.; Elena Fito, SF.; Alarcon, T. (2018). Noise-induced bistability in the quasi-neutral coexistence of viral RNAs under different replication modes. Journal of The Royal Society Interface. 15(142):1-10. https://doi.org/10.1098/rsif.2018.0129S11015142Sardanyés, J., Solé, R. V., & Elena, S. F. (2009). Replication Mode and Landscape Topology Differentially Affect RNA Virus Mutational Load and Robustness. Journal of Virology, 83(23), 12579-12589. doi:10.1128/jvi.00767-09Thébaud, G., Chadœuf, J., Morelli, M. J., McCauley, J. W., & Haydon, D. T. (2009). The relationship between mutation frequency and replication strategy in positive-sense single-stranded RNA viruses. Proceedings of the Royal Society B: Biological Sciences, 277(1682), 809-817. doi:10.1098/rspb.2009.1247Sardanyés, J., Martínez, F., Daròs, J.-A., & Elena, S. F. (2011). Dynamics of alternative modes of RNA replication for positive-sense RNA viruses. Journal of The Royal Society Interface, 9(69), 768-776. doi:10.1098/rsif.2011.0471Martínez, F., Sardanyés, J., Elena, S. F., & Daròs, J.-A. (2011). Dynamics of a Plant RNA Virus Intracellular Accumulation: Stamping Machine vs. Geometric Replication. Genetics, 188(3), 637-646. doi:10.1534/genetics.111.129114García-Villada, L., & Drake, J. W. (2012). The Three Faces of Riboviral Spontaneous Mutation: Spectrum, Mode of Genome Replication, and Mutation Rate. PLoS Genetics, 8(7), e1002832. doi:10.1371/journal.pgen.1002832Schulte, M. B., Draghi, J. A., Plotkin, J. B., & Andino, R. (2015). Experimentally guided models reveal replication principles that shape the mutation distribution of RNA viruses. eLife, 4. doi:10.7554/elife.03753Chao, L., Rang, C. U., & Wong, L. E. (2002). Distribution of Spontaneous Mutants and Inferences about the Replication Mode of the RNA Bacteriophage φ6. Journal of Virology, 76(7), 3276-3281. doi:10.1128/jvi.76.7.3276-3281.2002Combe, M., Garijo, R., Geller, R., Cuevas, J. M., & Sanjuán, R. (2015). Single-Cell Analysis of RNA Virus Infection Identifies Multiple Genetically Diverse Viral Genomes within Single Infectious Units. Cell Host & Microbe, 18(4), 424-432. doi:10.1016/j.chom.2015.09.009Schulte, M. B., & Andino, R. (2014). Single-Cell Analysis Uncovers Extensive Biological Noise in Poliovirus Replication. Journal of Virology, 88(11), 6205-6212. doi:10.1128/jvi.03539-13Gutiérrez, S., Michalakis, Y., & Blanc, S. (2012). Virus population bottlenecks during within-host progression and host-to-host transmission. 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Central limit theorems and diffusion approximations for multiscale Markov chain models. The Annals of Applied Probability, 24(2), 721-759. doi:10.1214/13-aap934Anderson, D. F., & Kurtz, T. G. (2015). Stochastic Analysis of Biochemical Systems. doi:10.1007/978-3-319-16895-1Gillespie, D. T. (1976). A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics, 22(4), 403-434. doi:10.1016/0021-9991(76)90041-3Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry, 81(25), 2340-2361. doi:10.1021/j100540a008Luria, S. E. (1951). THE FREQUENCY DISTRIBUTION OF SPONTANEOUS BACTERIOPHAGE MUTANTS AS EVIDENCE FOR THE EXPONENTIAL RATE OF PHAGE REPRODUCTION. Cold Spring Harbor Symposia on Quantitative Biology, 16(0), 463-470. doi:10.1101/sqb.1951.016.01.033Sardanyés, J. (2014). Viral RNA Replication Modes: Evolutionary and Dynamical Implications. 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Coexistence and critical behaviour in a lattice model of competing species

In the present paper we study a lattice model of two species competing for the same resources. Monte Carlo simulations for d=1, 2, and 3 show that when resources are easily available both species coexist. However, when the supply of resources is on an intermediate level, the species with slower metabolism becomes extinct. On the other hand, when resources are scarce it is the species with faster metabolism that becomes extinct. The range of coexistence of the two species increases with dimension. We suggest that our model might describe some aspects of the competition between normal and tumor cells. With such an interpretation, examples of tumor remission, recurrence and of different morphologies are presented. In the d=1 and d=2 models, we analyse the nature of phase transitions: they are either discontinuous or belong to the directed-percolation universality class, and in some cases they have an active subcritical phase. In the d=2 case, one of the transitions seems to be characterized by critical exponents different than directed-percolation ones, but this transition could be also weakly discontinuous. In the d=3 version, Monte Carlo simulations are in a good agreement with the solution of the mean-field approximation. This approximation predicts that oscillatory behaviour occurs in the present model, but only for d>2. For d>=2, a steady state depends on the initial configuration in some cases.Comment: 11 pages, 14 figure

The type II phase resetting curve is optimal for stochastic synchrony

The phase-resetting curve (PRC) describes the response of a neural oscillator to small perturbations in membrane potential. Its usefulness for predicting the dynamics of weakly coupled deterministic networks has been well characterized. However, the inputs to real neurons may often be more accurately described as barrages of synaptic noise. Effective connectivity between cells may thus arise in the form of correlations between the noisy input streams. We use constrained optimization and perturbation methods to prove that PRC shape determines susceptibility to synchrony among otherwise uncoupled noise-driven neural oscillators. PRCs can be placed into two general categories: Type I PRCs are non-negative while Type II PRCs have a large negative region. Here we show that oscillators with Type II PRCs receiving common noisy input sychronize more readily than those with Type I PRCs.Comment: 10 pages, 4 figures, submitted to Physical Review

Stationary states for underdamped anharmonic oscillators driven by Cauchy noise

Using methods of stochastic dynamics, we have studied stationary states in the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape of stationary states depend both on the potential type and the damping. If the damping is strong enough, for potential wells which in the overdamped regime produce multimodal stationary states, stationary states in the underdamped regime can be multimodal with the same number of modes like in the overdamped regime. For the parabolic potential, the stationary density is always unimodal and it is given by the two dimensional $\alpha$-stable density. For the mixture of quartic and parabolic single-well potentials the stationary density can be bimodal. Nevertheless, the parabolic addition, which is strong enough, can destroy bimodlity of the stationary state.Comment: 9 page

Coherence Resonance in Chaotic Systems

We show that it is possible for chaotic systems to display the main features of coherence resonance. In particular, we show that a Chua model, operating in a chaotic regime and in the presence of noise, can exhibit oscillations whose regularity is optimal for some intermediate value of the noise intensity. We find that the power spectrum of the signal develops a peak at finite frequency at intermediate values of the noise. These are all signatures of coherence resonance. We also experimentally study a Chua circuit and corroborate the above simulation results. Finally, we analyze a simple model composed of two separate limit cycles which still exhibits coherence resonance, and show that its behavior is qualitatively similar to that of the chaotic Chua systemComment: 4 pages (including 4 figures) LaTeX fil

Instability of insulating states in optical lattices due to collective phonon excitations

The role of collective phonon excitations on the properties of cold atoms in optical lattices is investigated. These phonon excitations are collective excitations, whose appearance is caused by intersite atomic interactions correlating the atoms, and they do not arise without such interactions. These collective excitations should not be confused with lattice vibrations produced by an external force. No such a force is assumed. But the considered phonons are purely self-organized collective excitations, characterizing atomic oscillations around lattice sites, due to intersite atomic interactions. It is shown that these excitations can essentially influence the possibility of atoms to be localized. The states that would be insulating in the absence of phonon excitations can become delocalized when these excitations are taken into account. This concerns long-range as well as local atomic interactions. To characterize the region of stability, the Lindemann criterion is used.Comment: Latex file, 27 pages, 1 figur

Research of the power plant operational states with block structure

In this article the research technique block structure power plant operational states is offered. As an example the operating power plant of OOO Siberian Generation Company with block structure of turbogenerators connection is considered. The choice of the operating power plant has allowed to receive to carry out the analysis real long and emergency states. The offered technique of states identification and the analysis can be used for power plant of other structure after the corresponding correction