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References 1. Bouchet, A. & Cuilleret, J. (1991). Bifurcation trahéale. In: Anatomie topographique, descriptive et fonctionnelle. Le cou. Le torax. (pp. 1064-1065). Paris: Ed. Simep 2. Testut, L. (1921). Artère pulmonaire. In: Traité d’anatomie humaine. Angeiologie. (pp. 503-505). Paris: Ed. Gastoin Doin 3. Testut, L. (1949). Conduit trachéo-bronchic. In: Traité d’Anatomie Humaine. Livre III. Appareil de la respiration ét de la phonation. (pp. 788-804). Paris: Ed. Gaston Doin 4. Rouvière, H. & Delmas, A. (1991). Artère pulmonaire. Trachée. Bronches In: Anatomie

, C., Ott, E. and Yorke, J.A. (1983). Crises, sudden changes in chaotic attractors, and transient chaos, Physica D: Nonlinear Phenomena 7 (1-3): 181-200. Grebogi, C., Ott, E. and Yorke, J.A. (1986). Critical exponent of chaotic transients in nonlinear dynamical systems, Physical Review Letters 57 (11): 1284-1287. Grebogi, C., Ott, E., Romeiras, F. and Yorke, J.A. (1987). Critical exponents for crisis-induced intermittency, Physical Review A 36 (11): 5365-5380. Guckenheimer, J. and Holmes, P. (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations

References Bhattacharyya, R. and Mukhopadhyay, B. (2006). Spatial dynamics of nonlinear prey-predator models with prey migration and predator switching, Ecological Complexity   3 (2): 160-169. Faria, T. (2001). Stability and bifurcation for a delayed predatorprey model and the effect of diffusion, Journal of Mathematical Analysis and Applications   254 (2): 433-463. Gao, S. J., Chen, L. S. and Teng, Z. D. (2008). Hopf bifurcation and global stability for a delayed predator-prey system with stage structure for predator, Applied Mathematics and Computation   202

References Bischi, G.I., Gardini, L. (2000). Global Properties of Symmetric Competition Models with Riddling and Blowout Phenomena. Discrete Dynamics in Nature and Society. Vol. 5, 149-160. Day, R.H. (1994). Complex Economic Dynamics. The MIT Press, Cambridge, Massachusetts. Elaydi, S. (1996). An Introduction to Difference Equations. Springer, New York. Elaydi, S. (2008). Discrete Chaos: With Applications in Science and Engineering. Chapman and Hall/CRC. Guzowska, M., Luis, R., Elaydi, S. (2011). Bifurcation and invariant manifolds of the logistic

laboratory system using stepper motor. Journal of Mechanical Engineering – Strojnícky časopis 2009 (60), No 4., 211 – 220. [4] B. S. Cazzolato, Z. Prime. On the dynamics of the furuta pendulum. Journal of Control Science and Engineering 2011 , p. 8. Article ID 528341. DOI: 10.1155/2011/528341 [5] M. B. Vizi, G. Stepan. Experimental Bifurcation Diagram of Furuta Pendulum, Paper No. DSCC2018-9030, ASME 2018 DSCC Atlanta, Georgia, USA, Sept. 30-Okt 4., 2018 . [6] J. Stein, R. Chmúrny. Comparison of phenomenological methods for dry-friction simulation of an oscillatory

References [1] YAZDANI, A.-MARIESA, L.-GUO, J. : An Improved Nonlinear STATCOM Control for Electric Arc Furnace Voltage Flicker Mitigation, IEEE Trans. On Power Delivery 24 No. 4 (2009), 2284-2290. [2] WANG, Y. F.-JIANG, J. G.-GE, L. S.-YANG, X. J. : Mitigation of Electric Arc Furnace Voltage Flicker using Static Synchronous Compensator, Proc. IEEE Power Electronics and Motion Control Conf No. 3 (2006), 1-5. [3] ROSEHART, W. D.-CAN, C. A.-ZARES, I. : Bifurcation Analysis of Various Power System Models, Int. J. Elect. Power Energy Syst. 21 No. 3 (1999), 171

References [1] Śloderbach Z. (1980): Bifurcations criteria for equilibrium states in generalized thermoplasticity [in Polish], Ph.D. thesis. – IFTR Reports, Institute of Fundamental Technological Research, Polish Academy of Sciences, nr 37/1980, Warsaw, pp.1-100. [2] Śloderbach Z. (1983): Generalized coupled thermoplasticity. Part I. Fundamental equations and identities. – Archives of Mechanics, No.35, vol.3, pp.337-349. [3] Śloderbach Z. (1983): Generalized coupled thermoplasticity. Part II. On the uniqueness and bifurcations criteria. – Archives of

. Appl. Math. 27 (1974), 193-211. [5] Babuska, I., Osborn, J.: Eigenvalue problems , in “Handbook of numerical analysis”, Vol. II, North- Holland, Amsterdam, (1991), 314-787. [6] Beurling, A., Livingston, A.: A theorem on duality mappings in Banach space, Ark. Mat. 4 (1962), 405-411. [7] Binding, P. A., Huang, Y. X.: Bifurcation from eigencurves of the p-Laplacian, Diff. Int. Equations 8 no. 2 (1995), 415-418. [8] Browder, F. E.: On a theorem of Beurling and Livingston , Cand. J. Math. 17 (1965), 367-372. [9] Browder, F. E., Fixed point theory and nonlinear

− = u − is equivalent to the existence of a periodic orbit. Once introduced the systems under study and having defined in a precise way how the different orbits behave, our goal is to analyze the existence of periodic orbits and characterize their bifurcations. To this end, after some preliminary results that appear in Section 2 , we present our main results in Section 3 , see Theorem 9 . Such theorem implies that, in the particular saddle case under study, periodic orbits appear either through heteroclinic bifurcations or through saddle-node bifurcations

References [1] AUGER, P.-PARRA, R. B-MORAND, S.-SÁNCHEZ, E.: A predator-prey model with predators using hawk and dove tactics, Mathematical Biosciences 177&178 (2002), 185-200. [2] KUZNETSOV, Y. A.: Elements of Applied Bifurcation Theory. Springer-Verlag, Berlin, New York, Inc. 1998.