Research interests

• Machine learning
• Dynamical systems
• Differential equations
• Reaction-diffusion equations
• Hyperbolic attractors
• Systems with dry friction

Projects

• Hysteretic neural networks
• Reaction-diffusion systems: hysteresis and nonlocal interactions
  (Project A9 of the DFG Collaborative Research Center 910 on Control of self-organizing nonlinear systems)

Begun N., Kravetc P., Rachinskii D. 
Chaos in Saw Map 
Submitted, arXiv 1709.01962 (2018)
(pdf) 

Begun N., Pliss V. A., Sell G. 
On the stability of weakly hyperbolic invariant sets 
Journal of Differential Equations, Vol. 262, No. 4, pp. 3194-3213. 2017. 
(pdf)

Arnold M., Begun N., Gurevich P., Kwame E., Lamba H., Rachinskii D.
Dynamics of discrete time systems with a hysteresis stop operator. 
SIAM Journal on Applied Dynamical Systems. Vol. 16, No. 1, pp. 91-119. 2017 
(pdf)

Begun N., Pliss V. A., Sell G. 
On the stability of hyperbolic attractors of systems of differential equations 
Differential Equations. Vol. 52, No. 2, pp. 139-148. 2016 
(pdf)

Begun N. 
Perturbations of weakly hyperbolic invariant sets of two-dimensional periodic systems.   
Vestnik St. Petersburg University: Mathematics, Vol. 48, No 1, pp. 1-8 (2015) 
(pdf)

Begun N., Kryzhevich S.
One-dimensional chaos in a system with dry friction: analytical approach 
Meccanica, Vol. 50, No. 8, pp. 1935-1948 (2015) 
(pdf)

Begun N. 
On the stability of invariant sets of leaves of three-dimensional periodic systems. 
Vestnik St. Petersburg University. Mathematics, Vol. 47, No. 3, pp. 95-101. 2014. 
(pdf)

Begun N.
On the closure of the leaf invariant set of perturbed system. 
Differential Equations and Control Processes. No 1. 80-88. 2013. 
(pdf)

Begun N. 
On the stability of sheet invariant sets of swo-dimensional periodic systems. 
Vestnik St. Petersburg University. Mathematics, Vol. 45, No. 4, pp. 145-152. 2012. 
(pdf)

Begun N., Pilyugin S. Yu. 
Analogues of Takens theorems for generalized actions of the group Z^∞. 
Vestnik St. Petersburg University. Mathematics, Vol. 43, No. 4, pp. 198-203. 2010. 
(pdf)

Begun N.
On the existence of square-integrable solutions for systems with weak nonlinearity. 
Vestnik St. Petersburg University. Mathematics, Vol. 43, No. 2, pp. 74-81. 2010. 
(pdf)