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Estimation of synaptic activity during neuronal oscillations
(Multidisciplinary Digital Publishing Institute (MDPI), 2020-11-24)
Article
Open AccessIn the study of brain connectivity, an accessible and convenient way to unveil local functional structures is to infer the time trace of synaptic conductances received by a neuron by using exclusively information about its ... -
Canard-induced complex oscillations in an excitatory network
(2020-01-01)
Article
Open AccessIn Neuroscience, mathematical modelling involving multiple spatial and temporal scales can unveil complex oscillatory activity such as excitable responses to an input current, subthreshold oscillations, spiking or bursting. ... -
Darboux integrability and dynamics of the Basener–Ross population model
(Circolo Matematico di Palermo, 2020)
Article
Open AccessWe deal with the Basener and Ross model for the evolution of human population in Easter island. We study the Darboux integrability of this model and characterize all its global dynamics in the Poincaré disc, obtaining 15 ... -
Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies
(2020-01-01)
Article
Open AccessWe study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum. We consider a 3-dimensional torus ... -
On planar polynomial vector fields with elementary first integrals
(2019-10-05)
Article
Restricted access - publisher's policyWe show that under rather general conditions a polynomial differential system having an elementary first integral already must admit a Darboux first integral, and we explicitly characterize the vector fields in this class. ... -
Critical velocity in kink-defect interaction models: rigorous results
(2020-01-01)
Article
Open AccessIn this work we study a model of interaction of kinks of the sine-Gordon equation with a weak defect. We obtain rigorous results concerning the so-called critical velocity derived in [7] by a geometric approach. More ... -
Study of periodic orbits in periodic perturbations of planar reversible Filippov systems having a twofold cycle
(2020-01-01)
Article
Open AccessWe study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed ... -
A general mechanism of diffusion in hamiltonian systems: qualitative results
(2019-01-01)
Article
Open AccessWe present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach is based on following the “outer dynamics” along homoclinic orbits to a ... -
The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability
(2019-12-01)
Article
Open AccessWe study the dynamics arising when two identical oscillators are coupled near a Hopfbifurcation where we assume a parameter uncouples the system at = 0. Using anormal form forN= 2 identical systems undergoing Hopf bifurcation, ... -
Hopf-Zero singularities truly unfold chaos
(2020-05-01)
Article
Restricted access - publisher's policyWe provide conditions to guarantee the occurrence of Shilnikov bifurcations in analytic unfoldings of some Hopf-Zero singularities through a beyond all order phenomenon: the exponentially small breakdown of invariant ... -
Dynamics in a time-discrete food-chain model with strong pressure on preys
(2020-05-01)
Article
Restricted access - publisher's policyDiscrete-time dynamics, mainly arising in boreal and temperate ecosystems for species with non-overlapping generations, have been largely studied to understand the dynamical outcomes due to changes in relevant ecological ... -
A geometric approach to phase response curves and its numerical computation through the parameterization method
(2019-01-01)
Article
Open AccessThe phase response curve (PRC) is a tool used in neuroscience that measures the phase shift experienced by an oscillator due to a perturbation applied at different phases of the limit cycle. In this paper, we present a new ...
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