Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise

Valenti, Davide; Augello, Giuseppa; Spagnolo, Bernardo

doi:10.1140/epjb/e2008-00315-6

Cited by 87 publications

(36 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More generally, it is one of the rare cases for which the steadystate density can be calculated for a two-dimensional stochastic system that does not obey detailed balance (for other examples, see [2] and [45]). It is conceivable that the method developed in our paper can also be applied to other two-dimensional systems [46] with simple piecewise constant or linear drift terms, e.g., the piecewise-linear FitzHugh-Nagumo model [47][48][49]. In each stripe of the phase space with continuous dynamics, the stationary probability density can be approximately calculated close to a one-dimensional manifold using a WKB ansatz if the noise is weak or the time-scale separation between slow and fast variables is large.…”

Section: Discussionmentioning

confidence: 99%

Analytical approach to an integrate-and-fire model with spike-triggered adaptation

Schwalger

Lindner

2015

Phys. Rev. E

View full text Add to dashboard Cite

The calculation of the steady-state probability density for multidimensional stochastic systems that do not obey detailed balance is a difficult problem. Here we present the analytical derivation of the stationary joint and various marginal probability densities for a stochastic neuron model with adaptation current. Our approach assumes weak noise but is valid for arbitrary adaptation strength and time scale. The theory predicts several effects of adaptation on the statistics of the membrane potential of a tonically firing neuron: (i) a membrane potential distribution with a convex shape, (ii) a strongly increased probability of hyperpolarized membrane potentials induced by strong and fast adaptation, and (iii) a maximized variability associated with the adaptation current at a finite adaptation time scale.

show abstract

Section: Discussionmentioning

confidence: 99%

Analytical approach to an integrate-and-fire model with spike-triggered adaptation

Schwalger

Lindner

2015

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…Moreover, in recent years, several theoretical investigations have focused on the positive effects of the noise on nonlinear systems, showing that, under suitable conditions, the addition of external fluctuations to intrinsically noisy systems may induce an enahncement of the dynamical stability of the system, resulting in a less noisy response [18][19][20][21][22][23][24][25][26][27][28]. This counterintuitive effect has been found in different physical areas, ranging from the generation of spin currents [29], aggregation kinetics of Brownian particles [30,31], chemical reaction system [32], translocation dynamics of polymers [33][34][35], ultra-fast magnetization dynamics of magnetic spin systems [36,37], dynamic electron response in zinc-blende semiconductor crystals [38][39][40][41][42][43], noise redistribution in quasi 2D Silicon Mos inversion layers [44], to interdisciplinary physical models [45][46][47][48][49][50][51][52].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Relaxation Phenomena in Metastable Condensed Matter Systems

Spagnolo

Guarcello

Magazzù

et al. 2016

Entropy

100

View full text Add to dashboard Cite

Nonlinear relaxation phenomena in three different systems of condensed matter are investigated. (i) First, the phase dynamics in Josephson junctions is analyzed. Specifically, a superconductor-graphene-superconductor (SGS) system exhibits quantum metastable states, and the average escape time from these metastable states in the presence of Gaussian and correlated fluctuations is calculated, accounting for variations in the the noise source intensity and the bias frequency. Moreover, the transient dynamics of a long-overlap Josephson junction (JJ) subject to thermal fluctuations and non-Gaussian noise sources is investigated. Noise induced phenomena are observed, such as the noise enhanced stability and the stochastic resonant activation. (ii) Second, the electron spin relaxation process in a n-type GaAs bulk driven by a fluctuating electric field is investigated. In particular, by using a Monte Carlo approach, we study the influence of a random telegraph noise on the spin polarized transport. Our findings show the possibility to raise the spin relaxation length by increasing the amplitude of the external fluctuations. Moreover, we find that, crucially, depending on the value of the external field strength, the electron spin depolarization length versus the noise correlation time increases up to a plateau. (iii) Finally, the stabilization of quantum metastable states by dissipation is presented. Normally, quantum fluctuations enhance the escape from metastable states in the presence of dissipation. We show that dissipation can enhance the stability of a quantum metastable system, consisting of a particle moving in a strongly asymmetric double well potential, interacting with a thermal bath. We find that the escape time from the metastable region has a nonmonotonic behavior versus the system-bath coupling and the temperature, producing a stabilizing effect.Keywords: metastability; nonequilibrium statistical mechanics and nonlinear relaxation time; noise enhanced stability; Josephson junction; spin polarized transport in semiconductors; open quantum systems; quantum noise enhanced stability

show abstract

“…In fact, cancer growth dynamics is a typical example of complex dynamics in which the role of fluctuations can be relevant, as in biological systems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Intermittent targeted therapies and stochastic evolution in patients affected by chronic myeloid leukemia

Pizzolato¹,

Adorno²,

Valenti³

et al. 2016

J. Stat. Mech.

View full text Add to dashboard Cite

Abstract. Front line therapy for the treatment of patients aected by chronic myeloid leukemia (CML) is based on the administration of tyrosine kinase inhibitors, namely imatinib or, more recently, axitinib. Although imatinib is highly eective and represents an example of a successful molecular targeted therapy, the appearance of resistance is observed in a proportion of patients, especially those in advanced stages. In this work, we investigate the appearance of resistance in patients aected by CML, by modeling the evolutionary dynamics of cancerous cell populations in a simulated patient treated by an intermittent targeted therapy. We simulate, with the Monte Carlo method, the stochastic evolution of initially healthy cells to leukemic clones, due to genetic mutations and changes in their reproductive behavior. We first present the model and its validation with experimental data by considering a continuous therapy. Then, we investigate how fluctuations in the number of leukemic cells aect patient response to the therapy when the drug is administered with an intermittent time scheduling. Here we show that an intermittent therapy (IT) represents a valid choice in patients with high risk of toxicity, despite an associated delay to the complete restoration of healthy cells. Moreover, a suitably tuned IT can reduce the probability of developing resistance.

show abstract

Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise

Cited by 87 publications

References 18 publications

Analytical approach to an integrate-and-fire model with spike-triggered adaptation

Analytical approach to an integrate-and-fire model with spike-triggered adaptation

Nonlinear Relaxation Phenomena in Metastable Condensed Matter Systems

Intermittent targeted therapies and stochastic evolution in patients affected by chronic myeloid leukemia

Contact Info

Product

Resources

About