Towards Accurate PWL Approximations of Parameter-Dependent Nonlinear Dynamical Systems With Equilibria and Limit Cycles

2007 ◽  
Vol 54 (3) ◽  
pp. 620-631 ◽  
Author(s):  
Marco Storace ◽  
Federico Bizzarri
Keyword(s):  
Dynamical Systems ◽  
Limit Cycles ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Parameter Dependent

NOISE-INDUCED BACKWARD BIFURCATIONS OF STOCHASTIC 3D-CYCLES

2010 ◽  
Vol 09 (01) ◽  
pp. 89-106 ◽  
Author(s):  
I. BASHKIRTSEVA ◽  
L. RYASHKO ◽  
P. STIKHIN
Keyword(s):  
Dynamical Systems ◽  
Limit Cycles ◽  
Noise Intensity ◽  
Nonlinear Dynamical Systems ◽  
Period Doubling ◽  
Sensitivity Function ◽  
Function Technique ◽  
Stochastic Bifurcation ◽  
Nonlinear Dynamical ◽  
General Method

We study stochastically forced multiple limit cycles of nonlinear dynamical systems in a period-doubling bifurcation zone. Noise-induced transitions between separate parts of the cycle are considered. A phenomenon of a decreasing of the stochastic cycle multiplicity with a noise intensity growth is investigated. We call it by a backward stochastic bifurcation (BSB). In this paper, for the BSB analysis we suggest a stochastic sensitivity function technique. As a result, a method for the estimation of critical values of noise intensity corresponding to BSB is proposed. The constructive possibilities of this general method for the detailed BSB analysis of the multiple stochastic cycles of the forced Roessler system are demonstrated.

scholarly journals Data-driven Evolution Equation Reconstruction for Parameter-Dependent Nonlinear Dynamical Systems

2018 ◽  
Vol 58 (6-7) ◽  
pp. 787-794 ◽  
Author(s):  
David W. Sroczynski ◽  
Or Yair ◽  
Ronen Talmon ◽  
Ioannis G. Kevrekidis
Keyword(s):  
Dynamical Systems ◽  
Evolution Equation ◽  
Nonlinear Dynamical Systems ◽  
Data Driven ◽  
Nonlinear Dynamical ◽  
Parameter Dependent
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