Ponossov, Arkadi

Professor

E-mail: arkadi.ponossov@umb.no

Phone: +47-6496-5468

Present position: Professor (Norwegian University of Life Sciences, UMB).

Degrees: PhD in mathematics at the Yekaterinburg State University (Russia), 1983.

Professional background: Perm State University, Russia: lecturer (1983-1985), senior lecturer (1986), associate professor (1986-1988) in mathematics; Perm State Technical University, Russia: senior research associate (1988-1990); Ruhr-Universität Bochum, Germany:  Alexander von Humboldt – research fellow (1990-1992),  Deutsche Forschungsgemeinschaft – research fellow (1992-1995); Norwegian University of Life Sciences:  professor in applied mathematics (1995 - )    

Research experience: Theoretical mathematics: Nonlinear functional analysis, almost periodic functions, stochastic differential equations, delay differential equations, multivalued functions, nonstandard analysis, non-commutative geometry, group theory. Applied mathematics: Control theory, hybrid dynamical systems, nonlinear dynamical systems, stability analysis, population dynamics, gene regulatory networks, Levenberg-Marquart methods and nonlinear estimation.

Experience in R&D management: Coordinator of a Norwegian-Mozambican research and education project (1998 - present).

Current research activity: Qualitative analysis of gene regulatory networks with and without delay and stochastic effects. Power-law formalism in biology: theoretical analysis and parameter estimation. Neural networks: firing-rate models and mathematical justification of those. Supervision of 4 PhD students.

Selected publications:

  • M. Drakhlin, A. Ponossov, E. Stepanov (2002). On some classes of operators determined by the structure of their memory. Proceedings of the Edinburgh Mathematical Society. Cambridge University Press, v. 45 (2), p. 467-490
  • E. Litsyn, Y. Nepomnyashikh, A. Ponossov (2002). Dynamical systems with hybrid feedback control as functional differential equations. International Journal of Hybrid Systems, v. 2 (1), p. 1-21.
  • A. Ponossov, J. Miguel, A. Shindiapin (2002). The W-transform links delay and ordinary differential equations. Israel J. Func. Diff. Equations, v. 9, no. 3-4, p. 40-73
  • Ponossov, A. Shindiapin (2003). Azbelev’s W-transform and its applications in mathematical modelling. Differential Eqs and Control Processes, v. 4, p. 1-21
  • E. Litsyn, M. Myasnikova, Y. Nepomnyashikh, A. Ponossov (2004). Efficient criteria for stabilization of planar linear systems by hybrid feedback controls. Abstract and Applied Analysis, v. 6, p. 487-499.
  • R. Kadiev, A. Ponossov (2004). Stability of stochastic functional differential equations and the W-transform. Electronic Journal of Differential Equations, v. 92, pp. 1-36.
  • Ponossov, J. Miguel, A. Shindiapin (2004). Parameter estimation for differential equation with delay. Transactions of Russian Academy of Natural Sciences, v. 3, no. 3-4, p. 135-143
  • E. Litsyn, Y. Nepomnyashikh, A. Ponossov (2005). Hybrid feedback stabilization of quasilinear systems in the plane. J. Math. Analysis Appl, v. 305, no. 1, p. 347-366.
  • R. Kadiev, A. Ponossov (2005). Relations between stability and admissibility for stochastic linear functional differential equations. Israel J. Func. Diff. Equations, v. 12, no. 1-2, p. 209-244
  • Ponossov (2005). Gene regulatory networks and delay differential equations. Electronic Journal of Differential Equations, v. 12, pp. 117-141.
  • Ponossov, Y. Nepomnyashchikh, A. Shindiapin (2005). Stability analysis for systems with logoid-nonlinearities and distributed delay. Transactions of Russian Academy of Natural Sciences, v. 9, no. 1-2, p. 78-94
  • E. Litsyn, Y. Nepomnyashikh, A. Ponossov (2006). Control of the Lyapunov exponents of dynamical systems in the plane with incomplete observation. Nonlinear Analysis: Hybrid Systems and Applications 64, no. 2, p. 329-351
  • A. Ponossov, R. Kadiev (2006). Linear stochastic functional differential equations: stability, admissible pairs of spaces and N.V.Azbelev’s W-method. Problems of Nonlinear Analysis in Engineering Systems 25, no. 1, p. 57-89
  • A. Ponossov, Y. Nepomnyashchikh, A. Shindiapin (2006). Stability analysis of systems with switch-like interactions and distributed delays: a case study. Israel J. Func. Diff. Equations, v. 13, no. 3-4, p. 539-570
  • M. Drakhlin, E. Litsyn, A. Ponossov, E. Stepanov (2006). Generalizing the property of locality: atomic/coatomic operators and applications. J. of Nonlinear and Convex Analysis, v. 7, no. 2, p. 139-162
  • R. Kadiev, A. Ponossov (2007). Stability of Solutions of Linear Impulsive Systems of Itˆo Differential Equations with Aftereffect. Differential Equations, v. 43, no. 7, p. 898-904.
  • I. Shlykova, A. Ponossov, Y. Nepomnyashchikh, A. Shindiapin (2008). A general framework for stability analysis of gene regulatory networks with delay. Electronic Journal of Differential Equations, v. 104, pp. 1-36.
  • R. Kadiev, A. Ponossov (2008). Exponential stability of linear stochastic differential equations with bounded delay and the W-transform. E. J. Qualitative Theory of Diff. Eqs, v. 23, p. 1-14.
  • R. Kadiev, A. Ponossov (2008). Partial Lyapunov Stability of Linear Stochastic Functional Differential Equations With Respect to Initial Values. Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis, v. 15, no. 5, p. 727-754.