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A complete definition of complexity for individual organisms, species, ecosystems, biological evolution and the biosphere has eluded researchers, and still is an ongoing issue.
Most complex system models are often formulated in terms of concepts drawn from statistical physics, information theory and non-linear dynamics; however, such approaches are not focused on, or do not include, the conceptual part of complexity related to organization and topological attributes or algebraic topology, such as network connectivity of genomes, interactomes and biological organisms that are very important. Recently, the two complementary approaches based both on information theory, network topology/abstract graph theory concepts are being combined for example in the fields of neuroscience and human cognition. It is generally agreed that there is a hierarchy of complexity levels of organization that should be considered as distinct from that of the levels of reality in ontology. The hierarchy of complexity levels of organization in the biosphere is also recognized in modern classifications of taxonomic ranks, such as: biological domain and biosphere, biological kingdom, Phylum, biological class, order, family, genus and species. Because of their dynamic and composition variability, intrinsic "fuzziness", autopoietic attributes, ability to self-reproduce, and so on, organisms do not fit into the 'standard' definition of general systems, and they are therefore 'super-complex' in both their function and structure; organisms can be thus be defined in CSB only as 'meta-systems' of simpler dynamic systems Such a meta-system definition of organisms, species, 'ecosystems', and so on, is not equivalent to the definition of a system of systems as in Autopoietic Systems Theory,; it also differs from the definition proposed for example by K.D. Palmer in meta-system engineering, organisms being quite different from machines and automata with fixed input-output transition functions, or a continuous dynamical system with fixed phase space, contrary to the Cartesian philosophical thinking; thus, organisms cannot be defined merely in terms of a quintuple A of (states, startup state, input and output sets/alphabet, transition function), although 'non-deterministic automata', as well as 'fuzzy automata' have also been defined. Tessellation or cellular automata provide however an intuitive, visual/computational insight into the lower levels of complexity, and have therefore become an increasingly popular, discrete model studied in computability theory, applied mathematics, physics, computer science, theoretical biology/systems biology, cancer simulations and microstructure modeling. Evolving cellular automata using genetic algorithms is also an emerging field attempting to bridge the gap between the tessellation automata and the higher level complexity approaches in CSB.
^ abRosen, R. (1958b). "The Representation of Biological Systems from the Standpoint of the Theory of Categories". Bulletin of Mathematical Biophysics. 20: 317–341. doi:10.1007/bf02477890.
^ abcdBaianu, I. C.; Brown, R.; Glazebrook, J. F. (2007). "Categorical Ontology of Complex Spacetime Structures: The Emergence of Life and Human Consciousness". Axiomathes. 17: 223–352. doi:10.1007/s10516-007-9011-2.
^Heylighen, Francis (2008). "Complexity and Self-Organization". In Bates, Marcia J.; Maack, Mary Niles. Encyclopedia of Library and Information Sciences. CRC. ISBN 978-0-8493-9712-7
^^ Heylighen, Francis (2008). "Complexity and Self-Organization". In Bates, Marcia J.; Maack, Mary Niles. Encyclopedia of Library and Information Sciences. CRC. ISBN 978-0-8493-9712-7
^The Evolutionary Design of Collective Computation in Cellular Automata, James P. Crutchfeld, Melanie Mitchell, Rajarshi Das (In J. P. Crutchfield and P. K. Schuster (editors), Evolutionary Dynamics|Exploring the Interplay of Selection, Neutrality, Accident, and Function. New York: Oxford University Press, 2002.)
^Evolving Cellular Automata with Genetic Algorithms: A Review of Recent Work, Melanie Mitchell, James P. Crutchfeld, Rajarshi Das (In Proceedings of the First International Conference on Evolutionary Computation and Its Applications (EvCA'96). Moscow, Russia: Russian Academy of Sciences, 1996.)
^Rosen, R. 1960. (1960). "A quantum-theoretic approach to genetic problems". Bulletin of Mathematical Biophysics. 22 (3): 227–255. doi:10.1007/BF02478347.
^Baianu, I. C.: 2006, (2006). "Robert Rosen's Work and Complex Systems Biology". Axiomathes. 16 (1–2): 25–34. doi:10.1007/s10516-005-4204-z.CS1 maint: Multiple names: authors list (link)
^Rosen, R.: 1958b, (1958). "The Representation of Biological Systems from the Standpoint of the Theory of Categories". Bulletin of Mathematical Biophysics. 20 (4): 317–341. doi:10.1007/BF02477890.CS1 maint: Multiple names: authors list (link)
Ahmed, E. (2006). "On modeling the immune system as a complex system". Theor. BioSci. 124: 413.
Baianu, I. C., Computer Models and Automata Theory in Biology and Medicine., Monograph, Ch.11 in M. Witten (Editor), Mathematical Models in Medicine, vol. 7., Vol. 7: 1513-1577 (1987),Pergamon Press:New York, (updated by Hsiao Chen Lin in 2004 ISBN 0-08-036377-6
Bonner, J. T. 1988. The Evolution of Complexity by Means of Natural Selection. Princeton: Princeton University Press.
Donald Snooks, Graeme, "A general theory of complex living systems: Exploring the demand side of dynamics", Complexity, vol. 13, no. 6, July/August 2008.
Kampen, N.G. van. Stochastic Processes in Physics and Chemistry, North Holland., 3rd ed. 2001, ISBN 0-444-89349-0
Murray, J.D., Mathematical Biology. Springer-Verlag, 3rd ed. in 2 vols.: Mathematical Biology: I. An Introduction, 2002 ISBN 0-387-95223-3; Mathematical Biology: II. Spatial Models and Biomedical Applications, 2003 ISBN 0-387-95228-4.
Nicolas Rashevsky. (1938)., Mathematical Biophysics. Chicago: University of Chicago Press.
Preziosi, L., Cancer Modelling and Simulation. Chapman Hall/CRC Press, 2003. ISBN 1-58488-361-8.
Renshaw, E., Modelling biological populations in space and time. C.U.P., 1991. ISBN 0-521-44855-7
Rosen, Robert.1991, Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life, Columbia University Press, published posthumously:
Rosen, Robert .1970. Dynamical system theory in biology. New York, Wiley-Interscience. ISBN 0-471-73550-7
Rosen, Robert. 2000, Essays on Life Itself, Columbia University Press.