Extreme bursting events via pulse-shaped explosion in mixed Rayleigh-Liénard nonlinear oscillator

Bursting in a Subcritical Hopf Oscillator with a Nonlinear Feedback

Bursting is a periodic transition between a quiescent state and a state of repetitive spiking. The phenomenon is ubiquitous in a variety of neurophysical systems. We numerically study the dynamical properties of a normal form of subcritical Hopf oscillator (at the bifurcation point) subjected to a nonlinear feedback. This dynamical system shows an infinite-period or a saddle-node on a limit cyc...

Active Distribution Networks Restoration after Extreme Events

After extreme events such as floods, thunderstorms, blizzards and hurricanes there will be devastating effects in the distribution networks which may cause a partial or complete blackout. Then, the major concern for the system operators is to restore the maximum critical loads as soon as possible by available generation units.  In order to solve this problem, this paper provides a restoration s...

Factorization technique and isochronous condition for coupled quadratic and mixed Liénard-type nonlinear systems

In this paper, we discuss a systematic and self consistent procedure to factorize a rather general class of coupled nonlinear ordinary differential equations (ODEs), namely coupled quadratic and mixed Liénard type equations, which include various physical and mathematical models. The procedure is broadly divided into two parts. In the first part, we consider a general factorized form for the eq...

Approximate solution of a mixed nonlinear stochastic oscillator

Pulse shaping and ultrashort laser pulse filamentation for applications in extreme nonlinear optics

English abstract This thesis deals with numerical studies of the properties and applications of spatio-temporally coupled pulses, conical wavepackets and laser filaments, in strongly nonlinear processes, such as harmonic generation and pulse reshaping. We study the energy redistribution inside these wavepackets propagating in gases and condensed media, in the linear and nonlinear regime. The en...