Jürgen Jost
Publikationen

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Telefon:
+49 (0) 341 - 9959 - 550

Fax:
+49 (0) 341 - 9959 - 555

Email

Addresse:
Inselstr. 22
04103 Leipzig
Deutschland

Dynamical systems

1. Textbooks

2. Morse-Conley theory

  • H. J. Fan and J. Jost. Conley index theory and Novikov-Morse theory. Pure and Applied Mathematics Quarterly, 1(4):939-971, 2005. (see PDF, 270 Kb)
  • H.J. Fan and J. Jost. Novikov-Morse theory for dynamical systems. Calc. Var., (17):29-73, 2003.
  • J. Jost. Orientable and nonorientable minimal surfaces. In Proceedings of the First World Congress of Nonlinear Analysts, Tampa, Florida, pages 819-826, Berlin - New York, August 19-26 1992. Walter de Gruyter.
  • J. Jost and M. Struwe. Morse-Conley theory for minimal surfaces of varying topological type. Invent. math., (102):465-499, 1990.

Topics

Morse-Conley theory for minimal surfaces

Morse-Novikov-Conley

3. Nonlinear dynamics, synchronization

  • W.L. Lu, F. Atay, and J. Jost. Consensus and synchronization in delayed networks of mobile multi-agents.
  • J. Jost, F. Atay, S. Jalan. Symbolic dynamics and synchronization of coupled map networks with multiple delay. Physics Letters A, 2010.
  • B. Gutkin, T. Hely, and J. Jost. Noise delays onset of sustained firing in a minimal model of persistent activity. Neurocomputing, (58-60):753-760, 2004. (see PDF, 445 Kb)
  • F. Bauer, F. Atay, and J. Jost. Synchronization in discrete-time networks with general pairwise coupling. Nonlinearity, 22:2333-2351, 2009.
  • W.L. Lu, F. Atay, and J. Jost. Consensus and synchronization in discrete-time networks of multi-agents with markovian jump topologies and delays, 2009.
  • W.L. Lu, F. Atay, and J. Jost. Chaos synchronization in networks of coupled maps with time-varying topologies. Eur. Phys. J. B, 63:399-406, 2008.
  • F. Atay, T. Bıyıkoğlu, and J. Jost. Network synchronization: Spectral versus statistical properties. Physica D, (224):35-41, 2006.
  • J. Jost. Dynamical Networks . In Proceedings der Konferenz From Biology to Theory, Beijing, April 2005. in Lecture Notes in Computer Science, 2007.
  • W.L. Lu, F. Atay, and J. Jost. Synchronization of discrete-time dynamical networks with time varying couplings. SIAM J.Math.Anal., 39:1231-1259, 2007.
  • S. Jalan, F. Atay, and J. Jost. Inferring global synchrony from local symbolic dynamics. 2006. Proc. ECCS.
  • F. Atay, S. Jalan, and J. Jost. Randomness, chaos, and structure. Complexity, (15):29-35, 2009.
  • S. Jalan, F. Atay, and J. Jost. Detecting global properties of coupled dynamics using local symbolic dynamics. Chaos, 16(033124):1-9, 2006.
  • F. Atay, S. Jalan, and J. Jost. Symbolic dynamics and synchronization of coupled map networks with multiple delays. Phys.Lett.A, 2010.
  • S. Jalan, F. M. Atay, and J. Jost. Detection of synchronized chaos in coupled map networks using symbolic dynamics. eprint arXiv:nlin/0510057, 2005.
  • J. Jost and K.M. Kolwankar. Fractal stationary density in coupled maps. In J. Lévy-Véhel and E. Lutton, editors, Fractals in Engineering, pages 57-64. Springer, 2006.
  • J. Jost and K.M. Kolwankar. Global analysis of synchronization in coupled maps. Intern. J. Bifur. Chaos, 16(12):3695-3703, 2006.
  • F. Atay, T. Bıyıkoğlu, and J. Jost. Synchronization of networks with prescribed degree distributions. IEEE Transactions on Circuits and Systems - I: Regular Papers, 53(1):92-98, 2006. (see PDF, 160Kb)
  • F.M. Atay and J. Jost. On the emergence of complex systems on the basis of the coordination of complex behaviors of their elements. Complexity (2004):17-22, 10.
  • F.M. Atay, J. Jost, and A. Wende. Delays, connection topology, and synchronization of coupled chaotic maps. Phys. Rev. Lett., 92(144101), 2004. (see PDF, 380 Kb)
  • J. Jost and M. P. Joy. Evolving networks with distance preferences. Physical Review E, 66(036126):7 pages, 2002. (see PDF, 172 Kb)
  • J. Jost and M. P. Joy. Spectral properties and synchronization in coupled map lattices. Phys. Rev. E, 65(016201):1-9, 2002. (see PDF, 750 Kb)

Topics

Synchronization of coupled map lattices

chaos synchronization

role of transmission delays

relation between local and global dynamics

relation between dynamics and network structure

4. Learning dynamics

  • Q.S. Ren, K. Kolwankar, A. Samal, and J. Jost. Network motifs in STDP-driven neuronal networks.
  • Q.S. Ren, K. Kolwankar, A. Samal, and J. Jost. STDP-driven networks and the C. elegans neuronal network. Physica A, 389:3900-3914, 2010.
  • J. Jost and K. Kolwankar. Evolution of network structure by temporal learning. Physica A, 388:1959-1966, 2009.

Topics

Spike-time dependent synaptic plasticity and network evolution

5. Cellular automata

  • T. Rohlf and J. Jost. Dynamics of 1-d cellular automa with distance-dependent delays. Proceedings AUTOMATA'2010.

6. Complexity

  • J. Jost, N. Bertschinger, and E. Olbrich. Emergence. A dynamical systems approach. New Ideas Psych., (28):265-273, 2010.
  • T. Kahle, E. Olbrich, J. Jost, and N. Ay. Complexity measures from interaction structures. Phys. Rev. E, 79(026201), 2009.
  • F. M. Atay and J. Jost. On the emergence of complex systems on the basis of the coordination of complex behaviors of their elements. Complexity, (2004):17-22, 10. (see PDF, 2000 Kb)
  • J. Jost. On the notion of complexity. Theory Bioscienc., (117):161-171, 1998. (see PDF, 156 Kb)

Topics

Complexity measures (see also under "System theory")

emergence in dynamical systems

7. General surveys

  • F. Atay and J. Jost. Handbook of Statistical Systems Biology, chapter Qualitative inference for dynamical systems. Wiley.
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