In this study, we examine the bifurcation scenarios of a two-dimensional Hindmarsh-Rose type model [Tsuji et al., 2007] with four parameters and simulate some resemblances of neurophysiological features for this model using spike-and-reset conditions. We present possible classifications based on the results of the following assessments: 1) the number and stability of the equilibrium points are ...

Transients in ecology are extremely important since they determine how equilibria approached. The debate on the dynamic stability of ecosystems has been largely focused equilibrium states. However, constantly changing due to climate conditions or perturbations driven by crisis anthropogenic actions (habitat destruction, deforestation, defaunation), it is study dynamics can proceed till equilibr...

Functional connectivity is a fundamental property of neural networks that quantifies the segregation and integration of information between cortical areas. Due to mathematical complexity, a theory that could explain how the parameters of mesoscopic networks composed of a few tens of neurons affect the functional connectivity is still to be formulated. Yet, many interesting problems in neuroscie...

Mecynocera clausi I.C. Thompson, 1888 is the type genus and species of the monotypic family Mecynoceridae Andronov, 1973. Based on the first description of male mouthparts of Mecynocera clausi Thompson, 1888 (Copepoda: Calanoida), evidence is presented for the transfer of this genus and species to the Paracalanidae Giesbrecht, 1893. Thus, Mecynoceridae Andronov, 1973 becomes a junior synonym of...

Our previous work has shown that AFP could adjust synaptic conductance of RA network with its firing pattern changed from bursting to tonic firing, eventually leading song degradation. However, it is difficult explore the dynamic due high dimensionality and complexity. To address this issue, we use mean field theory proposed by Wilten Nicola reduce a system switching ordinary differential equat...

Boundary equilibria bifurcation (BEB) arises in piecewise-smooth (PWS) systems when an equilibrium collides with a discontinuity set under parameter variation. Singularly perturbed BEB refers to arising singular perturbation problems which limit as some ? 0 PWS undergo BEB. This work completes classification for codimension-1 singularly the plane initiated by present authors [19], using combina...

This special issue presents a selection of papers from the conference “Dynamics, Bifurcations and Strange Attractors” dedicated to the memory of Leonid Pavlovich Shilnikov (1934–2011) to commemorate his contributions to the theory of dynamical systems and bifurcations. The conference was held at the Lobachevsky State University of Nizhny Novgorod, Russia, on 1–5 July 2013. The conference was at...