Journal Articles

Janson, N and Marsden, CJ (2021) Optimization with delay-induced bifurcations, Chaos, 31(11), 113126, ISSN: 1054-1500. DOI: 10.1063/5.0058087.

Janson, N and Marsden, CJ (2021) Delay-induced homoclinic bifurcations in modified gradient bistable systems and their relevance to optimization, Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(9), 093120, ISSN: 1054-1500. DOI: 10.1063/5.0035959.

Janson, N and Kloeden, PE (2021) Robustness of a dynamical systems model with a plastic self-organising vector field to noisy input signals, The European Physical Journal Plus, 136(7), 720, DOI: 10.1140/epjp/s13360-021-01662-y.

Janson, N and Kloeden, PE (2020) Mathematical consistency and long-term behaviour of a dynamical system with a self-organising vector field, Journal of Dynamics and Differential Equations, 34(1), pp.63-78, ISSN: 1040-7294. DOI: 10.1007/s10884-020-09834-7.

Janson, N and Marsden, CJ (2017) Dynamical system with plastic self-organized velocity field as an alternative conceptual model of a cognitive system, Scientific Reports, 7, 17007, ISSN: 2045-2322. DOI: 10.1038/s41598-017-16994-y.

Janson, NB, Pototsky, A, Parkes, C (2013) Delayed feedback applied to breathing in humans, European Physical Journal: Special Topics, 222(10), pp.2623-2631, ISSN: 1951-6355. DOI: 10.1140/epjst/e2013-02042-7.

Janson, NB (2012) Non-linear dynamics of biological systems, Contemporary Physics, 53(2), pp.137-168, ISSN: 0010-7514. DOI: 10.1080/00107514.2011.644441.

Walsh, JL, Iza, F, Janson, N, Kong, MG (2012) Chaos in atmospheric-pressure plasma jets, PLASMA SOURCES SCIENCE & TECHNOLOGY, 21(3), p.034008, ISSN: 0963-0252. DOI: 10.1088/0963-0252/21/3/034008.

Law, VJ, O’Neill, FT, Dowling, DP, Walsh, JL, Iza, F, Janson, NB, Kong, MG (2011) Decoding of atmospheric pressure plasma emission signals for process control, Chaotic Modeling and Simulation, 1, pp.69-69.

Samardak, AS, Nogaret, A, Janson, NB, Balanov, A, Farrer, I, Ritchie, DA (2011) Spiking computation and stochastic amplification in a neuron-like semiconductor microstructure, Journal of Applied Physics, 109(10), pp.102408-1/5, ISSN: 0021-8979. DOI: 10.1063/1.3577609.

Pototsky, A, Janson, NB, Marchesoni, F, Saveliev, S (2010) Dimer currents on one dimensional asymmetric substrates, Chemical Physics, 375(?), pp.458-463, ISSN: 0301-0104. DOI: 10.1016/j.chemphys.2010.03.021.

Samardak, A, Nogaret, A, Janson, NB, Balanov, A, Farrer, I, Ritchie, DA (2010) Noise induced amplification of sub-threshold pulses in multi-thread excitable semiconductor 'neurons', Physica E, 42(?), pp.2853-2856, ISSN: 1386-9477. DOI: 10.1016/j.physe.2009.12.017.

POTOTSKY, A and JANSON, N (2010) GLOBAL DYNAMICS IN NETWORKS OF 1D ELEMENTS WITH TIME DELAYED MEAN FIELD COUPLING SUBJECT TO NOISE: SYNCHRONIZATION THRESHOLD, MULTISTABILITY AND HYSTERESIS, International Journal of Bifurcation and Chaos, 20(06), pp.1825-1836, ISSN: 0218-1274. DOI: 10.1142/s0218127410026873.

Walsh, JL, Iza, F, Janson, NB, Law, VJ, Kong, MG (2010) Three Distinct Modes in a Cold Atmospheric Pressure Plasma Jet, Journal of Physics D: Applied Physics, 43(075201), pp.1-14, DOI: 10.1088/0022-3727/43/7/075201.

Pototskyy, A and Janson, NB (2010) Global dynamics in networks of 1D elements with time-delayed mean field coupling subject to noise: synchronization threshold, multistability and hysteresis, International Journal of Bifurcation and Chaos, 20(6), pp.1825-1836.

Pototsky, A, Janson, NB, Marchesoni, F, Savel'ev, S (2009) Dipole rectification in an oscillating electric field, EPL, 88(3), ARTN 30003, ISSN: 0295-5075. DOI: 10.1209/0295-5075/88/30003.

Samardak, A, Nogaret, A, Janson, NB, Balanov, A, Farrer, I, Ritchie, DA (2009) Noise-Controlled Signal Transmission in a Multihread Semiconductor Neuron, Physical Review Letters, 102(22), pp.226802-1/4, ISSN: 0031-9007. DOI: 10.1103/PhysRevLett.102.226802.

Pototskyy, A and Janson, NB (2009) Synchronization of a large number of continuous one-dimensional stochastic elements with time delayed mean field coupling, Physica D, 238, pp.175-183, ISSN: 0167-2789. DOI: 10.1016/j.physd.2008.09.010.

Pototskyy, A and Janson, NB (2009) Delay-induced spatial correlations in one-dimensional stochastic networks with nearest-neighbor coupling, Physical Review E, 80(6), Art.No. 066203.

Patidar, S, Pototskyy, A, Janson, NB (2009) Controlling noise-induced behavior of excitable networks, New J. Phys, 11, Art No. 073001.

Janson, NB, Balanov, AG, Schöll, E (2008) Control of Noise-Induced Dynamics, pp.221-273, DOI: 10.1002/9783527622313.ch11.

Pototskyy, A and Janson, NB (2008) Excitable systems with noise and delay with applications to control: renewal theory approach, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 77(3), Art No. 031113, ISSN: 1539-3755. DOI: 10.1103/PhysRevE.77.031113.

Pototskyy, A and Janson, NB (2008) Hysteresis and multistability in networks of bistable stochastic elements with global interaction, New Journal of Physics, 10, Art.No. 113006.

Pototsky, A and Janson, N (2007) Correlation theory of delayed feedback in stochastic systems below Andronov-Hopf bifurcation, Physical Review E, 76(5), 056208, ISSN: 1539-3755. DOI: 10.1103/physreve.76.056208.

Natsheh, AN, Kettleborough, JG, Janson, NB (2007) Experimental Study of Controlling Chaos in a DC-DC Boost Converter, Chaos, Solitons and Fractals, 40.

Pototskyy, A and Janson, NB (2007) Correlation theory of delayed feedback in stochastic systems below Andronov-Hopf bifurcation, Phys. Rev. E 056208, 76(3).

Hauschildt, B, Janson, NB, Balanov, A, Schoell, E (2006) Noise-induced cooperative dynamics and its control in coupled neuron models, PHYSICAL REVIEW E, 74(5), ARTN 051906, ISSN: 1539-3755. DOI: 10.1103/PhysRevE.74.051906.

Hauschildt, B, Janson, NB, Balanov, A, Schöll, E (2006) Noise-induced cooperative dynamics and its control in coupled neuron models, Physical review. E, Statistical, nonlinear, and soft matter physics, 74(5 Pt 1), p.051906, ISSN: 1539-3755.

Balanov, AG, Beato, V, Janson, NB, Engel, H, Schoell, E (2006) Delayed feedback control of noise-induced patterns in excitable media, PHYSICAL REVIEW E, 74(1), ARTN 016214, ISSN: 1539-3755. DOI: 10.1103/PhysRevE.74.016214.

Balanov, AG, Janson, NB, Scholl, E (2005) Delayed feedback control of chaos: Bifurcation analysis, Physical Review E, 71, pp.016222 (1-9), ISSN: 1095-3787. DOI: 10.1103/PhysRevE.71.016222.

Balanov, A, Janson, NB, Astakhov, V, McClintock, PVE (2005) Role of saddle tori in mutual synchronization of periodic oscillators, Phys. Rev. E, 72, Art. No. 026214.

Scholl, E, Balanov, AG, Janson, NB, Neiman, A (2005) Controlling stochastic oscillations close to a Hopf bifurcation by time-delayed feedback, Stochastics and Dynamics, 5, pp.281-295.

Janson, NB, Balanov, A, Scholl, E (2004) Delayed Feedback as a Means of Control of Noise-Induced Motion, Physical Review Letters, 93(1), pp.010601-1/4, ISSN: 0031-9007. DOI: 10.1103/PhysRevLett.93.010601.

Janson, NB, Balanov, A, Schoell, E (2004) Delayed feedback as a means of control of noise-induced motion, Physical Review Letters, 93, pp.Art.No. 010601(1-9), ISSN: 1079-7114. DOI: 10.1103/PhysRevLett.93.010601.

Schlesner, J, Amann, A, Janson, NB, Just, W, Scholl, E (2004) Publisher’s Note: Self-stabilization of high-frequency oscillations in semiconductor superlattices by time-delay autosynchronization [Phys. Rev. E68, 066208 (2003)], Physical Review E, 69(2), 029901, ISSN: 1539-3755. DOI: 10.1103/physreve.69.029901.

Balanov, A, Janson, NB, Schoell, E (2004) Control of noise-induced oscillations by delayed feedback, Physica D, 199, pp.1-2, ISSN: 0167-2789.

Schlesner, J, Amann, A, Janson, NB, Just, W, Scholl, E (2003) Self-stabilization of high-frequency oscillations in semiconductor superlattices by time-delay autosynchronization, PHYSICAL REVIEW E, 68(6), ARTN 066208, ISSN: 1539-3755. DOI: 10.1103/PhysRevE.68.066208.

Balanov, AG, Janson, NB, McClintock, PVE, Tucker, RW, Wang, CHT (2003) Bifurcation analysis of a neutral delay differential equation modelling the torsional motion of a driven drill string, Chaos, Solitions and Fractals, 15, pp.381-394, ISSN: 0960-0779.

Sherstnev, VV, Krier, A, Balanov, AG, Janson, NB, Silchenko, AN, McClintock, PVE (2003) Mid-infrared lasing induced by noise, Fluctuation and Noise Letters, 3(1), pp.K91-L95, ISSN: 0219-4775.

Balanov, AG, Janson, NB, McClintock, PVE (2003) Coherence Resonance of the Noise-Induced Motion on the Way to Breakdown of Synchronization in Chaotic Systems, Fluctuations and Noise Letters, 3(2), pp.L113-L120.

Janson, NB, Igosheva, NB, Balanov, AG, Glushkovskaya Semyachkina, O, Anishchenko, TG, McClintock, PVE (2003) Indices of Cariorespiratory Synchronization from Rat Blood Pressure Data, Izv. Vuz. Applied Nonlinear Dynamics, 11(3), pp.120-132, ISSN: 0869-6632.

Schlesner, J, Amann, A, Janson, NB, Just, W, Scholl, E (2003) Self-stabilization of chaotic domain oscillations in superlattices by time-delayed feedback control, Semiconductor Science and Technology, 19, pp.1-3.

Schlesner, J, Amann, A, Janson, NB, Just, W, Scholl, E (2003) Self-stabilization of high-frequency oscillations in semiconductor superlattices by time-delay autosynchronization, Physical Review E, 68, Art. No. 066208.

Rzeczinski, S, Janson, NB, Balanov, AG, McClintock, PVE (2002) Regions of cardiorespiratory synchronization in humans under paced respiration, Physical review. E, Statistical, nonlinear, and soft matter physics, 66(5), p.51909, ISSN: 1539-3755. DOI: 10.1103/PhysRevE.66.051909.

Balanov, AG, Janson, NB, Postnov, DE, McClintock, PVE (2002) Coherence resonance versus synchronization in a periodically forced self-sustained system, PHYSICAL REVIEW E, 65(4), ARTN 041105, ISSN: 2470-0045. DOI: 10.1103/PhysRevE.65.041105.

Janson, NB, Balanov, AG, Anishchenko, VS, McClintock, PVE (2002) Phase relationships between two or more interacting processes from one-dimensional time series. I. Basic theory, Physical Review E, 65(3), pp.Art.No. 036211(1-12), ISSN: 1095-3787. DOI: 10.1103/PhysRevE.65.036211.

Rzeczinski, S, Janson, NB, Balanov, AG, McClintock, PVE (2002) Regions of cardiorespiratory synchronization in humans under paced respiration, Physical Review E, 66, Art. No. 051909, ISSN: 1063-651X.

Janson, NB, Balanov, AG, Anishchenko, VS, McClintock, PVE (2002) Phase relationships between two or more interacting processes from one-dimensional time series. II. Application to heart-rate-variability data, PHYSICAL REVIEW E, 65(3), pp.036212-036212, DOI: 10.1103/PhysRevE.65.036212.

Janson, NB, Balanov, AG, Anishchenko, VS, McClintock, PVE (2001) Phase Synchronization between Several Interacting Processes from Univariate Data, Physical Review Letters, 86(9), pp.1749-1752, ISSN: 1079-7114. DOI: 10.1103/PhysRevLett.86.1749.

Janson, NB, Balanov, AG, Anishchenko, VS, McClintock, PVE (2001) Modelling the dynamics of anles of human R-R intervals, Physiol. Meas, 22, pp.565-579.

Janson, NB, Balanov, AG, Anishchenko, VS, McClintock, PVE (2001) Phase coherence diagnostics by one-dimension time series, Tech. Phys. Lett, 27, pp.987-990.

Janson, NB, Anishchenko, VS, Balanov, AG, Igosheva, NB, Bordyugov, GV (2000) Synchronization of cardiorhythm by weak external forcing, Discrete Dynamics in Nature and Society, 3(4), pp.201-206, DOI: 10.1155/S1026022600000194.

Janson, NB, Pavlov, AN, Anishchenko, VS, Gridnev, VI, Dovgalevsky, PY (2000) Diagnostic of cardio-vascular disease with help of largest Lyapunov exponent of RR-sequences, Chaos Solitons and Fractals, 11(5), pp.807-814, DOI: 10.1016/S0960-0779(98)00212-4.

Janson, NB, Igosheva, NB, Balanov, AG, Glushkovskaja-Semyachkina, OV, Anishchenko, TG (2000) Application of nonlinear dynamics methods for the analysis of blood pressure dynamics under normal and stressful conditions, Journal of Hypertension, 18(2), pp.S61-S61.

Janson, NB, Anishchenko, VS, Balanov, AG, Igosheva, NB, Bordyugov, GV (2000) Entrainment between heart rate and weak noninvasive forcing, International Journal of Bifurcation and Chaos, 10(10), pp.2339-2348, DOI: 10.1142/S0218127400001468.

Janson, NB, Postnov, DE, Balanov, AG, Mosekilde, E (1999) Homoclinic bifurcation as a mechanism of chaotic phase synchronization, Physical Review Letters, 83(10), pp.1942-1945, DOI: 10.1103/PhysRevLett.83.1942.

Pavlov, AN, Yanson, NB, Kapitaniak, T, Anishchenko, VS (1999) Reconstruction of dynamic systems using short signals, Technical Physics Letters, 25(6), pp.424-426, ISSN: 1063-7850. DOI: 10.1134/1.1262504.

Yanson, NB, Pavlov, AN, Kapitaniak, T, Anishchenko, VS (1999) Global reconstruction from nonstationary data, Technical Physics Letters, 25(5), pp.412-414, ISSN: 1063-7850. DOI: 10.1134/1.1262500.

Anishchenko, VS, Pavlov, AN, Yanson, NB (1998) Reconstruction of dynamic systems as applied to secure communications, Technical Physics, 43(12), pp.1401-1407, ISSN: 1063-7842. DOI: 10.1134/1.1259214.

Janson, NB, Pavlov, AN, Anishchenko, VS (1998) One method for restoring inhomogeneous attractors, International Journal of Bifurcation and Chaos, 8(4), pp.825-833, DOI: 10.1142/S0218127498000620.

Janson, NB, Pavlov, AN, Neiman, AB, Anishchenko, VS (1998) Reconstruction of dynamical and geometrical properties of chaotic attractors from threshold-crossing interspike intervals, PHYSICAL REVIEW E, 58(1), pp.R4-R7, DOI: 10.1103/PhysRevE.58.R4.

Janson, NB, Anishchenko, VS, Pavlov, AN (1998) Global reconstruction in the presence of a priori information, CHAOS SOLITONS AND FRACTALS, 9(8), pp.1267-1278.

Yanson, NB, Pavlov, AN, Balanov, AG, Anishchenko, VS (1996) Reconstructing a mathematical model as applied to an electrocardiogram, Technical Physics Letters, 22(8), pp.669-671, ISSN: 1063-7850.

Anishchenko, VS, Janson, NB, Pavlov, AN (1996) A method for reconstructing nonuniform attractors, Technical Physics Letters, 22(4), pp.265-267, ISSN: 1063-7850.

Anishchenko, VS, Janson, NB, Pavlov, AN (1996) Saddle focus in a model of the electrical activity of the human heart, Technical Physics Letters, 22(2), pp.168-170, ISSN: 1063-7850.

Janson, NB and Marsden, CJ (Accepted for publication) Self-shaping dynamical systems and learning.

Janson, NB and Marsden, CJ (Accepted for publication) Optimization by delay.

Conferences

Law, VJ, Dowling, DP, Walsh, JL, Iza, F, Janson, NB, Kong, MG (2011) Decoding of atmospheric pressure plasma emission signals for process control. In 4th Chaotic Modeling & Simulation International Conference, Crete, Greece.

Samardak, AS, Nogaret, A, Taylor, S, Janson, N, Balanov, A, Farrer, I, Ritchie, DA (2010) Regular pulsing induced by noise in a monolithic semiconductor neuron. In Caldas, MJ and Studart, N (ed) CP 1199, 29th International Conference on the Physics of Semiconductors, AIP Conference Proceedings, ? pp.523-524, DOI: 10.1063/1.3295539.

Walsh, JL, Iza, F, Jason, NB, Kong, MG (2010) Chaos in atmospheric pressure plasma jets. In 37th IOP Annual Conference on Plasma Physics, Windermere, UK, pp.61-62.

Samardak, A, Nogaret, A, Janson, NB, Balanov, A, Farrer, I, Richtie, DA (2010) Noise induced amplification of sub-threshold pulses in multi-thread excitable semiconductor 'neurons'. In Physica E - Low-dimensional Systems and Nanostructures, pp.2853-2856.

Janson, NB, Pototskyy, A, Patidar, S (2010) Delayed feedback control in stochastic excitable networks. In From physics to control through an emergent view. World Scientific Series on Nonlinear Science, Series B, p. 51.

Pototsky, A and Janson, N (2009) Two-state stochastic process with time delayed feedback: controlling noise-induced oscillations in excitable systems. In , IFAC Proceedings Volumes, pp.11-15, DOI: 10.3182/20090622-3-uk-3004.00005.

Natsheh, AN, Janson, NB, Kettleborough, JG (2008) Control of chaos in a DC-DC boost converter. In 30 June-2 July 2008, IEEE International Symposium on Industrial Electronics, ?? pp.317-322.

Natsheh, AN, Janson, NB, Kettleborough, JG (2008) Control of Chaos in a DC-DC Boost Converter. In IEEE International Symposium on Industrial Electronics, 2008 IEEE INTERNATIONAL SYMPOSIUM ON INDUSTRIAL ELECTRONICS, VOLS 1-5, Cambridge, ENGLAND, pp.120-+, ISBN: 978-1-4244-1665-3.

Pototskiyy, A and Janson, NB (2007) Two-state model of excitable system with time delayed feedback: renewal theory approach. In Book of Abstracts of Noise in Life 2007: Stochastic Dynamics in the Neurosciences, Dresden (Germany).

Janson, NB, Balanov, A, Scholl, E (2007) Delayed feedback control of chaos: bifurcations in a large range of feedback parameters. In PhysCon 2007, Book of Abstracts of the 3rd International IEEE Scientific Conference on Physics and Control, Potsdam, Germany, p.204.

Pototskiyy, A and Janson, NB (2007) Two-state model of excitable system with time delayed feedback: renewal theory approach. In PhysCon 2007, Book of Abstracts of the 3rd International IEEE Scientific Conference on Physics and Control, Potsdam (Germany), p.63.

Patidar, S, Pototskiyy, A, Janson, NB (2007) Controlling noise-induced patterns in an ensemble of globally coupled neural oscillators. In International Workshop, Book of Abstracts of Physics of Fluctuations far from Equilibrium, Dresden, Germany.

Janson, NB and Pototskiyy, A (2007) Two-state model of excitable system with time delayed feedback: renewal theory approach. In Book of Abstracts of Dynamics Days 2007, Loughborough (UK), p.104.

Janson, NB, Patidar, S, Pototskiyy, A (2007) Time-delayed feedback control of noise-induced dynamics in a model of a neural network. In Book of Abstracts of Dynamic Days 2007, Loughborough (UK), p.122.

Pototskiyy, A and Janson, NB (2007) Two-state model of excitable system with time delayed feedback: renewal theory approach. In Book of Abstracts of ICIAM07, Zurich, pp.308-308.

Patidar, S, Pototskyy, A, Janson, NB (2007) Control of noise-induced behavior in neural network. In Book of Abstracts of ICIAM07, Zurich, pp.316-317.

Beato, V, Balanov, AG, Janson, NB, Engel, H, Scholl, E (2005) Delayed feedback control of noise-induced patterns in excitable media. In Dymanic Days Europe 2005, Book of Abstracts of XXV, Berlin, Germany, p.168.

Hauschildt, B, Balanov, AG, Janson, NB, Scholl, E (2005) Using time-delayed feedback for control of dynamics in coupled coherence resonance oscillators. In Dynamics Days Europe 2005, Book of Abstracts XXV, Berlin, Germany, p.9.

Janson, NB, Balanov, AG, Scholl, E (2005) Control of noise-induced oscillations. In Book of Abstracts of XXV Dynamics Days Europe 2005, Book of Abstracts of XXV, Berlin, Germany, p.141.

Scholl, E, Pomplun, J, Amann, A, Balanov, A, Janson, NB (2005) Time-delay feedback control of nonlinear stochastic oscillations. In van Campen, DH, Lazurko, MD, van der Oever, WPJM (ed) ENOC-2005, Proc %th EUROMECH Nonlinear Dynamics Conference, Eindhoven, pp.208-237.

Balanov, A, Janson, NB, Wang, C, Wiercigroch, M (2002) Multiple delay differential systems in a sensing problem. In Report from a 43rd European Study Group with Industry, Lancaster, UK, pp.F1-F17.

Janson, NB, Balanov, A, Anishchenko, V, McClintock, PVE (2002) Phase synchronization from one-dimensional time series. In Book of Abstracts of Dynamics Days Europe 2002, Heidelberg, p.25.

Balanov, A, Janson, NB, Anishchenko, V, McClintock, PVE (2002) Phase relationships from one-dimensional signals. In Book of Abstracts of Synchro-2002, Saratov, Russia, p?.

Anishchenko, VS, Balanov, AG, Janson, NB, Igosheva, NB, Bordyugov, GV (2000) Synchronization of heart rate by sound and light pulses. In , STOCHASTIC AND CHAOTIC DYNAMICS IN THE LAKES, pp.162-167, ISBN: 1-56396-915-7.

Igosheva, NB, Janson, NB, Balanov, AG, Romanova, TP, Glushkovskaja-Semjachkina, OV, Anishchenko, TG, Anishchenko, VS (2000) Dynamics of blood pressure in healthy rats at rest and after stress. In , STOCHASTIC AND CHAOTIC DYNAMICS IN THE LAKES, pp.168-174, ISBN: 1-56396-915-7.

Pavlov, AN, Janson, NB, Anishchenko, VS (1997) Statistical approach to the problem of global reconstruction. In , International Conference on Control of Oscillations and Chaos, Proceedings, pp.315-316.

Janson, NB and Anishchenko, VS (1996) Modeling the dynamical systems on experimental data. In , CHAOTIC, FRACTAL, AND NONLINEAR SIGNAL PROCESSING, pp.688-708, ISBN: 1-56396-443-0.

Books

Balanov, AG, Janson, NB, Sosnovtseva, OV, Postnov, DE (2009) Synchronization: From Simple to Complex, Springer 2009, ISBN: 978-3-540-72127-7.

Chapters

Janson, NB (2011) Biosimulation in Biomedical Research, Health Care and Drug Development. In Sosnovtseva, O, Rostami-Hodjegan, A, Mosekilde, E (ed) Biosimulation in Biomedical Research, Health Care and Drug Development, Springer Verlag, pp.285-310, ISBN: 9783709104170.

Sosnovtseva, OV, Postnov, DE, Janson, NB, Balanov, A (2011) Synchronization: A Case in Biological Studies. In Mosekilde, E, Sosnovtseva, O, Rostami-Hodjegan, A (ed) Biosimulation in Biomedical Research, Health Care and Drug Development, Springer Verlag,ISBN: 9783709104170.

Janson, NB, Balanov, A, Scholl, E (2007) Control of noise-induced dynamics. In Scholl, E and Schuster, HG (ed) Handonbook of Chaos Control, Wiley-VCH, pp.223-273, ISBN: 3-527-40605-0.

Janson, NB, Pavlov, AN, Anishchenko, VS (2003) Global reconstruction: application to biological data and secure communication. In Gouerbet, G and Meunier Guttin Cluzel, S (ed) Chaos and its reconstruction, Novascience, pp.287-317, ISBN: 1-59033-805-7.

Datasets

Janson, N and Marsden, CJ (2022) Supplementary Information Files for Delay-induced homoclinic bifurcations in modified gradient bistable systems and their relevance to optimization, DOI: 10.17028/rd.lboro.18319820.

Other

Janson, NB and Marsden, CJ (Accepted for publication) Conceptual model of a cognitive system: dynamical system with plastic self-organizing velocity field, Spontaneously evolving living systems can be modelled as continuous-time dynamical systems (DSs), whose evolution rules are determined by their velocity vector fields. We point out that because of their architectural plasticity, biological neural networks belong to a novel type of DSs whose velocity field is plastic, albeit within bounds, and affected by sensory stimuli. We introduce DSs with fully plastic velocity fields self-organising under the influence of stimuli, called self-shaping DSs, and propose that a system of this class represents a conceptual model of a cognitive system. We propose a simple phenomenological model that within a single field-shaping mechanism carries out a set of essential cognitive functions without any supervision and online, just like living cognitive systems do. The performance of this model is illustrated experimentally with musical examples. Unlike in artificial neural networks, this mechanism does not produce spurious attractors and in principle does not limit memory size. Implementation of this principle could pave the way to creating artificial intelligent devices of a new type..

Janson, NB and Kloeden, PE (Accepted for publication) Asymptotic behaviour of dynamical systems with plastic self-organising vector fields, In [Janson & Marsden 2017] a dynamical system with a plastic self-organising velocity vector field was introduced, which was inspired by the architectural plasticity of the brain and proposed as a possible conceptual model of a cognitive system. Here we provide a more rigorous mathematical formulation of this problem, make several simplifying assumptions about the form of the model and of the applied stimulus, and perform its mathematical analysis. Namely, we explore the existence, uniqueness, continuity and smoothness of both the plastic velocity vector field controlling the observable behaviour of the system, and of the behaviour itself. We also analyse the existence of pullback attractors and of forward limit sets in such a non-autonomous system of a special form. Our results verify the consistency of the problem, which was only assumed in the previous work, and pave the way to constructing models with more sophisticated cognitive functions..

Janson, NB and Marsden, CJ (Accepted for publication) "Memory foam" approach to unsupervised learning, We propose an alternative approach to construct an artificial learning system, which naturally learns in an unsupervised manner. Its mathematical prototype is a dynamical system, which automatically shapes its vector field in response to the input signal. The vector field converges to a gradient of a multi-dimensional probability density distribution of the input process, taken with negative sign. The most probable patterns are represented by the stable fixed points, whose basins of attraction are formed automatically. The performance of this system is illustrated with musical signals..

Janson, NB and Marsden, CJ (Accepted for publication) Delay-induced homoclinic bifurcations in bistable dynamical systems, This paper is a prequel to our study of the possibility to solve global optimization problem by introducing a time delay into the classical gradient descent setting. Ultimately, we wish to explore the phenomena caused by delay in a dynamical system of the form $\dot{x}$$=$$f(x(t-\tau)$, $\tau$$>$$0$, where $f(z)$ is the negative of the gradient of some cost, or utility, function $V(z)$ with an arbitrary number of local minima of an arbitrary configuration. Using prior knowledge of the typical delay-induced effects in nonlinear dynamical systems, we hypothesize that the increase of delay should eliminate all local attractors and give rise to global chaos embracing all local minima, which could be exploited for optimization. In the subsequent paper studying multi-well $V(z)$ we demonstrate that this general idea has been correct. However, the details of bifurcations involved appear quite intricate and need to be first revealed for the simplest forms of utility functions having only two local minima, which is the goal of this paper. We discover that for a smooth $f$, the key phenomenon induced by the variation of the only control parameter $\tau$ is a homoclinic bifurcation coming in various versions. We reveal both the universal features of bifurcation scenarios realized for general smooth double-well landscapes $V$, and the distinctions between them determined by the local properties of $V$..