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An accuracy-based fuzzy classifier system (2004)
Presentation / Conference
Casillias, J., Carse, B., & Bull, L. (2004, June). An accuracy-based fuzzy classifier system. Paper presented at 12th Spanish Conference on Fuzzy Logic and Technologies

Correspondence between the temporal and spacial behavior in reversible one-dimensional cellular automata equivalent with the full shift (2004)
Presentation / Conference
Mora, J. C., Martinez, G. J., & McIntosh, H. V. (2004, June). Correspondence between the temporal and spacial behavior in reversible one-dimensional cellular automata equivalent with the full shift. Paper presented at DMCS Workshop

We present the basic properties of reversible one-dimensional cellular automata equivalent by permutations with the full shift, this work only takes reversible automata of neighborhood size 2. In these cases, we prove that the evolution rule defining... Read More about Correspondence between the temporal and spacial behavior in reversible one-dimensional cellular automata equivalent with the full shift.

Experimental implementation of mobile robot taxis with onboard Belousov-Zhabotinsky chemical medium (2004)
Journal Article
Ratcliffe, N., Adamatzky, A., Costello, B. D. L., Melhuish, C., & Ratcliffe, N. M. (2004). Experimental implementation of mobile robot taxis with onboard Belousov-Zhabotinsky chemical medium. Materials Science and Engineering: C, 24(4), 541-548. https://doi.org/10.1016/j.msec.2004.02.002

We discuss the first-ever experimental realization of the onboard excitable chemical controller for stimulus-guided navigation of mobile robots. We demonstrate that the Belousov-Zhabotinsky (BZ) reaction in the form of an onboard thin layer chemical... Read More about Experimental implementation of mobile robot taxis with onboard Belousov-Zhabotinsky chemical medium.

Reaction-diffusion navigation robot control: From chemical to VLSI analogic processors (2004)
Journal Article
Rodríguez-Vázquez, A., De Lacy Costello, B., Carmona-Galán, R., Arena, P., Adamatzky, A., Arena, P., …Rodriguez-Vazquez, A. (2004). Reaction-diffusion navigation robot control: From chemical to VLSI analogic processors. IEEE Transactions on Circuits and Systems I: Regular Papers, 51(5), 926-938. https://doi.org/10.1109/TCSI.2004.827654

We introduce a new methodology and experimental implementations for real-time wave-based robot navigation in a complex, dynamically changing environment. The main idea behind the approach is to consider the robot arena as an excitable medium, in whic... Read More about Reaction-diffusion navigation robot control: From chemical to VLSI analogic processors.

Voronoi diagrams generated by regressing edges of precipitation fronts (2004)
Journal Article
Hantz, P., De Lacy Costello, B. P., de Lacy Costello, B., Hantz, P., & Ratcliffe, N. M. (2004). Voronoi diagrams generated by regressing edges of precipitation fronts. Journal of Chemical Physics, 120(5), 2413-2416. https://doi.org/10.1063/1.1635358

The Voronoi diagram generated by regression edges of precipitation fronts was analyzed. In the reaction-diffusion system, one of the reagents penetrates into a gel by diffusion and forms a precipitate with the other reagent homogenized in the gel. It... Read More about Voronoi diagrams generated by regressing edges of precipitation fronts.

Sequential and continuum bifurcations in degenerate elliptic equations (2004)
Journal Article
Laister, R., Beardmore, R. E., & Laister, R. (2004). Sequential and continuum bifurcations in degenerate elliptic equations. Proceedings of the American Mathematical Society, 132(01), 165-174. https://doi.org/10.1090/S0002-9939-03-06979-X

We examine the bifurcations to positive and sign-changing solutions of degenerate elliptic equations. In the problems we study, which do not represent Fredholm operators, we show that there is a critical parameter value at which an infinity of bifurc... Read More about Sequential and continuum bifurcations in degenerate elliptic equations.

Finite time extinction in nonlinear diffusion equations (2004)
Journal Article
Beardmore, R. E., Peplow, A. T., & Laister, R. (2004). Finite time extinction in nonlinear diffusion equations. Applied Mathematics Letters, 17(5), 561-567. https://doi.org/10.1016/S0893-9659%2804%2990126-7

We consider a class of degenerate diffusion equations where the nonlinearity is assumed to be singular (non-Lipschitz) at zero. It is shown that solutions with compactly supported initial data become identically zero in finite time. Such extinction f... Read More about Finite time extinction in nonlinear diffusion equations.

The formation of voronoi diagrams in chemical and physical systems: Experimental findings and theoretical models (2004)
Journal Article
Ratcliffe, N., De Costello, B. L., Purwins, H. G., de Lacy Costello, B., Ratcliffe, N. M., Adamatzky, A., …Purwins, H. (2004). The formation of voronoi diagrams in chemical and physical systems: Experimental findings and theoretical models. International Journal of Bifurcation and Chaos, 14(7), 2187-2210. https://doi.org/10.1142/S021812740401059X

The work discusses the formation of Voronoi diagrams in spatially extended nonlinear systems taking experimental and theoretical results into account. Concerning experimental systems a number of chemical systems used previously as prototype chemical... Read More about The formation of voronoi diagrams in chemical and physical systems: Experimental findings and theoretical models.

Trajectories of a DAE near a pseudo-equilibrium (2004)
Journal Article
Laister, R., Beardmore, R. E., Laister, R., & Peplow, A. (2004). Trajectories of a DAE near a pseudo-equilibrium. Nonlinearity, 17(1), 253-279. https://doi.org/10.1088/0951-7715/17/1/015

We consider a class of differential-algebraic equations (DAEs) defined by analytic nonlinearities and study its singular solutions. The main assumption used is that the linearization of the DAE represents a Kronecker index-2 matrix pencil and that th... Read More about Trajectories of a DAE near a pseudo-equilibrium.