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Manjunath Gandhi

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Random difference equations: These equations arise as financial market models, epidemiology models, population biology, recurrent neural network models, discretization of stochastic dynamical systems, control theory and many more. More details on my research in this area can be found in  this web-tutorial (click here)


Research.  Some of my contributions are to:

  • Stability and "continuity" of solutions of time-varing networks of dynamical systems
  • Conley-decomposition theorem for Random Difference Equations
  • Zero-One Stability Law in Recurrent Neural Networks
  • Topology based denoing of chaotic time-series


Publications in Journals: 


  • G. Manjunath, H. Jaeger: The Dynamics of Random Difference Equations is Remodeled by Closed Relations. SIAM Journal on Mathematical Analysis 46(1), 459-483, 2014
  • G. Manjunath, H. Jaeger: Echo State Property Linked to an Input: Exploring a Fundamental Characteristic of Recurrent Neural Networks. Neural Computation Vol. 25, No. 3: 671–696, 2013
  • G. Manjunath and D. Fournier-Prunaret: Strong Persistence of an Attractor and Generalized Partial Synchronization in a Coupled Chaotic System. Chaos, 21(2), 023110, 2011
  • G. Manjunath and D. Fournier-Prunaret: Construction of Chaotic Maps on Nonconvex Spaces -- a Solution to a CSK Deciphering Problem. Int. J. Bifurcation and Chaos, 20(8), 2553--2559, 2010
  • G. Manjunath,  S. Sivaji Ganesh and G.V. Anand: Denoising Signals Corrupted by Chaotic Noise. Comm. Nonlinear Sci Numer. Simulat, 15(12), 3988-3997, 2010
  • G. Manjunath,  S. Sivaji Ganesh and G.V. Anand: Topology Based Denoising of Chaos. Dynamical Systems, An Int. Journal, 24(4), 501--516, 2009
  • G. Manjunath, D. Fournier-Prunaret and A. K. Taha: A 3-dimensional Piecewise Affine Map used as a Chaotic Generator.  Grazer Math. Ber., 354, 145--157, 2009
  • G. Manjunath and D. Fournier-Prunaret: A Qualitative Analysis of Deciphering Errors in Chaos Shift Keying. Int. J. Bifurcation and Chaos, 19, 2085--2092, 2009
  • G. Manjunath and O. Feely: On the Effect of the Integrator Initial State in a Non-ideal Sigma-Delta-Modulator.  Nonlinear Analysis : Real World applications, 10(5), 2799--2806, 2009
  • G. Manjunath, S. Sivaji Ganesh and G.V. Anand: Intra-Orbit Separation Properties of Dense Orbits of Interval Maps. Aequationes Mathematicae, 72,  89--99, 2006