The Algorithmic Analysis of Hybrid Systems

R. Alur C. Courcoubetis N. Halbwachs T. A. Henzinger P.-H. Ho X. Nicollin A. Olivero J. Sifakis S. Yovine 1995 The Algorithmic Analysis of Hybrid Systems Theoret. Comput. Sci. 138 1 3–34 10.1016/0304-3975(94)00202-T A. F. Atiya P. Baldi 1989 Oscillations and Synchronizations in Neural Networks: an Exploration of the Labeling Hypothesis Int. J. Neural Syst. 1 2 103–124 10.1142/S0129065789000025 A. Casagrande C. Piazza A. Policriti 2009 Discrete Semantics for Hybrid Automata Discrete Event Dyn. Syst. 19 4 471–493 10.1007/s10626-009-0082-7 A. Casagrande C. Piazza A. Policriti B. Mishra 2008 Inclusion dynamics hybrid automata Inform. and Comput. 206 12 1394–1424 10.1016/j.ic.2008.09.001 A. Dolzmann T. Sturm 1997 REDLOG: computer algebra meets computer logic SIGSAM Bull. 31 2 2–9 10.1145/261320.261324 H. B. Enderton 2001 A Mathematical Introduction to Logic II Harcourt/Academic Press M. Fränzle 1999 Analysis of Hybrid Systems: An Ounce of Realism Can Save an Infinity of States Int. Workshop on Computer, Science, and Logic (CSL 99) LNCS 1683 Springer 126–140 W. J. Freeman C. A. Skarda 1985 Spatial EEG patterns, non-linear dynamics and perception: the neo-Sherringtonian view. Brain Res 357 3 147–175 R. Ghosh C. Tomlin 2001 Lateral Inhibition through Delta-Notch signaling: A Piecewise Affine Hybrid Model Proc. of Hybrid Systems: Computation and Control (HSCC'01) LNCS 2034 Springer 232–246 10.1007/3-540-45351-2_21 A. Girard G. J. Pappas 2007 Approximation metrics for discrete and continuous systems IEEE Trans. Automat. Control 52 5 782–798 10.1109/TAC.2007.895849 C. M. Gray P. Konig A. K. Engel W. Singer 1989 Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties Nature 338 6213 334–337 10.1038/338334a0 R. Grosu G. Batt F. Fenton J. Glimm C. Guernic S. Smolka E. Bartocci 2011 From Cardiac Cells to Genetic Regulatory Networks Proc. of Computer Aided Verification (CAV'11) LNCS 6806 Springer 396–411 10.1007/978-3-642-22110-1_31 T. A. Henzinger P. W. Kopke A. Puri P. Varaiya 1995 What's decidable about hybrid automata? Proc. of ACM Symposium on Theory of Computing (STOCS'95) 373–382 10.1145/225058.225162 H. de Jong J.-L. Gouzé C. Hernandez M. Page T. Sari J. Geiselmann 2004 Qualitative simulation of genetic regulatory networks using piecewise-linear models Bulletin of Math. Biology 66 301–340 10.1016/j.bulm.2003.08.010 P. Prabhakar V. Vladimerou M. Viswanathan G. E. Dullerud 2009 Verifying Tolerant Systems Using Polynomial Approximations Proceedings of the 2009 30th IEEE Real-Time Systems Symposium RTSS '09 IEEE Computer Society

Washington, DC, USA

181–190 10.1109/RTSS.2009.28 S. Ratschan 2010 Safety Verification of Non-linear Hybrid Systems Is Quasi-Semidecidable Theory and Applications of Models of Computation (TAMC10) lncs 6108 springer 397–408 10.1007/978-3-642-13562-0_36 L. R. Silva Y. Amitai B. W. Connors 1991 Intrinsic oscillations of neocortex generated by layer 5 pyramidal neurons. Science 251 4992 432–5 10.1126/science.1824881 M. Steriade R. R. Llinás 1988 The functional states of the thalamus and the associated neuronal interplay. Physiological reviews 68 3 649–742 A. Tonnelier S. Meignen H. Bosch J. Demongeot 1999 Synchronization and desynchronization of neural oscillators Neural Networks 12 9 1213 – 1228 10.1016/S0893-6080(99)00068-4