En esta web se podrán encontrar todos aquellos aspectos relacionados con mi actividad investigadora que puedan resultar de interés.
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In this website, you can find all those aspects related to my research activities that may be of interest.

Research Specialties and interests

• Dynamical Systems
• Discrete Mathematics/Boolean networks
• Biomathematics

Honors and Awards

• Honorable Mention at the “Second International Competition for University Students of Mathematics”, Tempus European Project, Plovdiv (BULGARY), 1995.
• Award for the Best Work in Science, 2nd Doctoral Meeting of the region/state of Castilla-La Mancha (SPAIN), 2012.

Publications

Refereed/indexed articles (66)

1. F. Balibrea, J.C. Valverde, Bifurcations under nondegenerated conditions of higher degree and a new simple proof of the Hopf-Neimark-Sacker bifurcation theorem, J. Math. Anal. Appl. 237 (1999) 93-105.
2. J.C. Valverde, Topological Conjugations of Normal Forms in Bifurcations, Acta Math. Hungar 88 (2000) 113-121.
3. F. Balibrea, J.C. Valverde, Structural stability under conditions of non-hyperbolicity, Comput. Math. Appl. 41 (2001) 757-768
4. F. Balibrea, J.C. Valverde, Extreme degenerations for the simplest generic bifurcations and new transversally conditions, Discrete and Continuous Time Dynamical Systems 6 (2002) 22-30.
5. J.A. Aledo, J.C. Valverde, Applications of matrices and graphs in the Study of fuzzy relations; Bulletin of the Society Puig Adam 61 (2002) 59—72
6. F. Balibrea, J.C. Valverde, Topological normal forms of higher degree for the simplest bifurcations, Applied General Topology 2 (2002) 155-164.
7. J.C. Valverde et al, Instrumental versatility of number e, Bulletin of the Society Puig Adam 65 (2003) 77—93.
8. F. Balibrea, J.C. Valverde, Cusp and generalized flip bifurcations under higher degree conditions, Nonlinear Anal. Theor. 52 (2003) 405-419.
9. J.C. Valverde, F.L. Pelayo, J.A. Martinez, J.J. Miralles, Symbolic mathematical computing of bifurcations in dynamical Systems, Journal of Computational Methods in Sciences and Engineering 4 (2004) 115-123.
10. J.C. Valverde, F.L. Pelayo, J.A. Martinez, J.J. Miralles, Stability of continuous systems by Routh-Hurwitz and Mathematica, Journal of Computational Methods in Sciences and Engineering 4 (2004) 127-136.
11. J.C. Valverde, Simplest normal forms of Hopf-Neimark-Sacker bifurcations, Int. J. Bif. Chaos. 13 (2003) 1831-1839.
12. J.C. Valverde, L. Gardini, On the changes of periodicities in a piecewise linear rotation model. Appl. Math. Comput. 194 (2007) 381—388.
13. F. Balibrea, A. Martínez, J.C. Valverde, Local stabilility of contiuous dynamical systems in presence of non-hyperbolic equilibria, Int. J. Bif. Chaos 19 (2009) 1051—1057.
14. J.C. Valverde, Near a local topological equivalence when a quasi-center like point appears, Topology Appl. 156 (2009) 3016–3020.
15. F. Balibrea, A. Martínez, J.C. Valverde, Local bifurcations of continuous dynamical systems under higher order conditions, Appl. Math. Lett. 23 (2010) 230–234.
16. A Martínez, J.C. Valverde, Bifurcations of continuous dynamical systems under extreme and new transversality conditions, Appl. Math. Comput. 210 (2009) 33—38
17. J.L. García, F.L. Pelayo, J.C. Valverde, Modeling dynamics of concurrent computing systems, Comput. Math. Appl. 61 (2011) 1402—1406.
18. D. Aranda, D.Y. Trejos, J.C. Valverde, R. Villanueva, Modeling dynamics of Babesiosis disease in bovines and ticks populations, Math. Methods Appl. Sci. 35 (2012) 249—256.
19. J.A. Aledo, S. Martínez, F.L. Pelayo, J.C. Valverde, Parallel dynamical systems on maxterms and minterms Boolean functions, Math. Comput. Model. 55 (2012) 666—671.
20. F.L. Pelayo, J.C. Valverde, Notes on modeling dynamics of concurrent computing systems, Comput. Math. Appl. 64 (2012) 61—63.
21. A.M. Atehortua, L.M. Ladino, J.C. Valverde, Dsamala toolbox: software for the analysis and simulation of discrete, continuous and stochastic dynamical systems, Ing. Invest. 32 (2012) 51—57.
22. J.A. Aledo, S. Martinez, J.C. Valverde, Parallel dynamical systems over directed dependency graphs, Appl. Math. Comput. 219 (2012) 1114—1119.
23. J.A. Aledo, S. Martinez, J.C. Valverde, Parallel dynamical systems on independent local functions, J. Comput. Appl. Math. 237 (2013) 335—339.
24. L.M. Ladino, J.C. Valverde, Population dynamics of a two-stage species with recruitment, Math. Methods Appl. Sci. 36 (2013) 722-–729.
25. S. Martinez, J.C. Valverde, Location models applied to real-world problems, Modeling in Science and Education Learning, 6 (2) (2013) 91—104.
26. J.A. Aledo, S. Martinez, J.C. Valverde, Updating method for the computation of orbits in parallel dynamical systems, Int. J. Comput. Math 90 (9) (2013) 1796—1808.
27. J.A. Aledo, S. Martinez, J.C. Valverde, Parallel dynamical systems over special digraph classes, Int. J. Comput. Math 90 (10) (2013) 2039—2048.
28. A.M. Atehortua, L.M. Ladino, J.C. Valverde, Population dynamics of a two-stage migratory species with predation and capture, Nonlinear Anal.-Real World Appl. 16 (2014), 27—39.
29. A. Sadiq, F. Ahmad, S.A. Khan, J.C. Valverde. Modeling and analysis of departure routine in air traffic control based on Petri nets, Neural Comput. Appl., 25(5) (2014) 1099—1109
30. L.M. Ladino, E.I. Sabogal, J.C. Valverde, General functional response and recruitment in a predator-prey system with capture on both species, Math. Meth. Appl. Sci., 38(13) (2015) 2876–2887. doi: 10.1002/mma.3271.
31. J.A. Aledo, S. Martinez, J.C. Valverde, Graph dynamical systems with general Boolean states, Appl. Math. Inf. Sci. 9(4) (2015) 1803–1808. doi: 10.12785/amis/090417.
32. J.A. Aledo, S. Martinez, J.C. Valverde, Parallel dynamical systems over graphs and related topics: A survey, J. Appl. Maths 2015 (2015), Article ID 594294, 14 pages. doi: 10.1155/2015/594294.
33. L.M. Ladino, E.I. Sabogal, J.C. Valverde, Optimal control of a bioeconomic model for a two-stage species with recruitment, Appl. Math. Inf. Sci. 9(5) (2015) 2485–2492. doi: 10.12785/amis/090532.
34. L.M. Ladino, C. Mammana, E. Michetti, J.C. Valverde, Discrete time population dynamics of a two-stage species with recruitment and capture. Chaos, Solitons and Fractals 85 (2016) 143-150. doi: 10.1016/j.chaos.2016.01.032.
35. L.M. Ladino, C. Mammana, E. Michetti, J.C. Valverde, Border collision bifurcations in a generalized model of population dynamics, Discrete Dynamics in Nature and Society, vol. 2016, Article ID 9724139, 13 pages, 2016. doi:10.1155/2016/9724139.
36. S.A. Khan, D. He, J.C. Valverde, Pattern recognition in bioinformatics, BioMed Research International, vol. 2016, Article ID 5284169, 2 pages, 2016. doi:10.1155/2016/5284169.
37. F. Balibrea, H.M. Oliveira, J.C. Valverde, Topological equivalences for one-parameter bifurcations of scalar maps, J Nonlinear Sci. 27 (2) (2017) 661-685. doi: 10.1007/s00332-016-9347-0.
38. J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, On periods of parallel dynamical Systems, Complexity, Volume 2017, Article ID 7209762, 6 pages, doi: 10.1155/2017/7209762.
39. B. Ghosh, D. Pal, T.K. Kar , J.C. Valverde, Biological conservation through marine protected areas in the presence of alternative stable states, Math. Biosci. 286 (2017) 49–57 doi: 10.1016/j.mbs.2017.02.004
40. J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, On periods and equilibria of sequential dynamical systems, Inf. Sci. (2017), doi: 10.1016/j.ins.2017.05.002.
41. D.F. Aranda, D.Y. Trejos, J.C. Valverde, A discrete epidemic model for bovine Babesiosis disease and tick populations, Open Phys. 15 (2017) 360-369, doi: 10.1515/phys-2017-0040.
42. S. Cuomo, A. Galletti, L. Marcellino, J.C. Valverde, NAMDAC Numerical Algorithms and Methods for Data Analysis and Classification, Proceedings – 12th International Conference on Signal Image Technology and Internet-Based Systems, SITIS 2016, 21 April 2017, Article number 7907433, Page xxv, doi: 10.1109/SITIS.2016.6.
43. M.A. Khan, S. Islam, J.C. Valverde, S.A. Khan, Control Strategies of Hepatitis b with Three Control Variables, J. Biol. Syst. 26 (1) (2018) 1-21. doi:10.1142/S0218339018500018.
44. J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, «Predecessors and Gardens of Eden in sequential dynamical systems over directed graphs,» Applied Mathematics and Nonlinear Sciences 3(2) (2018) 593–602, doi: 10.2478/AMNS.2018.2.00046.
45. J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, Maximum number of periodic orbits in parallel dynamical systems, Inf. Sci. 468 (2018) 63–71, doi: 10.1016/j.ins.2018.08.041.
46. J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, Predecessors and Garden-of-Eden configurations in parallel dynamical systems on maxterm and minterm Boolean functions, J. Comput. Appl. Math. 348 (2019) 26–33, doi: 10.1016/j.cam.2018.08.015.
47. J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, Solution to the predecessors and Gardens-of-Eden problems for synchronous systems over directed graphs, Appl. Math. Comput. 370 (2019) 22–28, doi: 10.1016/j.amc.2018.10.077.
48. J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, Predecessors Existence Problems and Gardens of Eden in Sequential Dynamical Systems, Complexity, vol. 2019, Article ID 6280960, 10 pages, 2019, doi: 10.1155/2019/6280960.
49. J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, Dynamical attraction in parallel network models, Appl. Math. Comput. 361 (2019) 874-888, doi: 10.1016/j.amc.2019.05.048.
50. A. Galletti, L. Marcellino, S. Cuomo, J.C. Valverde, NAMDAC: Numerical algorithms and methods for data analysis and classification. Proceedings – 14th International Conference on Signal Image Technology and Internet Based Systems, SITIS 2018, (2019), XXVII, doi: 10.1109/SITIS.2018.00007.
51. M. Abdelheq, O. Belhamiti, L. Bouzid, D.Y. Trejos, J.C. Valverde, A predictive spatio-temporal model for bovine Babesiosis epidemic transmission, J. Theor. Biol. 480 (2019) 192-204, doi: 10.1016/j.jtbi.2019.07.015.
52. Q.A. Dang, M.T. Hoang, D.Y. Trejos, J.C. Valverde, Feedback control variables to restrain the Babesiosis disease, Math. Meth. Appl. Sci. 42(18) (2019) 7517-7527, doi: 10.1002/mma.5877.
53. J.C. Valverde, H.S. Mortveit, C. Gershenson, Y. Shi, Boolean Networks and Their Applications in Science and Engineering, Complexity Volume 2020, Article ID 6183798, doi: 10.1155/2020/6183798.
54. S. Kozerenko, J.C. Valverde, Periods in XOR parallel dynamical systems over directed dependency graphs, J. Comput. Appl. Math. 364 (2020) 112313, doi: 10.1016/j.cam.2019.06.029.
55. J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, Attractors and transient in sequential dynamical systems, Int. J. Comput. Math. 97(1-2) (2020) 467-481, doi: 10.1080/00207160.2019.1647338.
56. J.A. Aledo, A. Barzanouni, G. Malekbala, L. Sharifan, J.C. Valverde, On the Periodic Structure of Parallel Dynamical Systems on Generalized Independent Boolean Functions, Mathematics 8(7) (2020) 1088, doi: 10.3390/math8071088.
57. Q.A. Dang, M.T. Hoang, D.Y. Trejos, J.C. Valverde, Nonstandard Finite Difference Schemes for the Study of the Dynamics of the Babesiosis Disease, Symmetry 2020, 12, 1447, doi:10.3390/sym12091447.
58. J.A. Aledo, A. Barzanouni, G. Malekbala, L. Sharifan, J.C. Valverde, Counting Periodic Points in Parallel Graph Dynamical Systems, Complexity, Volume 2020, Article ID 9708347, 9 pages, doi:10.1155/2020/9708347.
59. J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs, Mathematics 2020, 8(10), 1812, doi: 10.3390/math8101812.
60. J.A. Aledo, S. Martinez, J.C. Valverde, Boolean Networks Models in Science and Engineering, Mathematics 2021, 9(8), 867, doi: 10.3390/math9080867.
61. J.A. Aledo, A. Barzanouni, G. Malekbala, L. Sharifan, J.C. Valverde, Existence, coexistence and uniqueness of fixed points in parallel and sequential dynamical systems over directed graphs, Communications in Nonlinear Science and Numerical Simulation 103 (2021) 105966, doi:10.1016/j.cnsns.2021.105966.
62. J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, Enumerating periodic orbits in sequential dynamical systems over graphs, J. Comput. Appl. Math. 405 (2022), 113084, doi: 10.1016/j.cam.2020.113084.
63. D.Y. Trejos, J.C. Valverde, E. Venturino, Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation, Applied Mathematics and Nonlinear Sciences 7(1) (2022) 1-26, doi:10.2478/AMNS.2021.1.00012.
64. J.A. Aledo, A. Barzanouni, G. Malekbala, L. Sharifan, J.C. Valverde, Fixed points in generalized parallel and sequential dynamical systems induced by a minterm or maxterm Boolean functions, J. Comput. Appl. Math. (2022), doi: 10.1016/j.cam.2021.114070.
65. J.A. Aledo, G. Manjabacas, J. Robles, J.C. Valverde, Fuzzy parallel dynamical systems on Zadeh operators, Mathematical Methods in the Applied Sciences 46(9) (2023) 10260 – 10267, doi: 10.1002/mma.9117.
66. J.A. Aledo, E. Goles, M. Montalva-Medel, P. Montealegre, J.C. Valverde, Symmetrizable Boolean networks, Information Sciences 626 (2023) 787–804, doi: 10.1016/j.ins.2023.01.082.

Recent Research Grants and Contracts

• Regional Government of Castilla-La Mancha, 09/30/2022-08/31/25, «Analysis of Science and Engineering Models». Role: Applicant/Principal Investigator
• Research funding of the University of Castilla-La Mancha, 04/01/23-03/31/25, “Dynamical Systems». Role: Applicant/Principal Investigator

Ph.D. Students (5)

1. A. Martinez, Polytechnic University of Valencia, SPAIN. «Analysis of non-standard bifurcation conditions for continuous dynamical systems», July 2010.
2. L.M. Ladino, University of Los Llanos, COLOMBIA, “Populations Dynamics of Migratory Species with recruitment, predation and capture», April 2013.
3. L.G. Díaz, University Autonoma of Madrid, Spain, “Advances in parallel and sequential dynamical systems over graphs and their applications”, February 2020.
4. D.Y. Trejos, University San Jose de Caldas, COLOMBIA «Dynamics of epidemiological models for the bovine babesiosis», (in progress).
5. Jose P. Llano, University of Valencia, SPAIN, (in progress)

Presentations

Invited talks

• International conference: Chaos and Dynamics in Biological Networks, France, June 2008
Presented (plenary session): “Bifurcations in discrete and continuous dynamical systems generalized.” Role: Main speaker/lecturer (invited)
• International conference: Trends in Bifurcation Analysis, Italy, June 2009.
Presented (plenary session): “Local Topological equivalences between entire and truncated normal forms.” Role: Invited speaker
• II International Conference on Applied Mathematics, Colombia, September 2014.
Presented (plenary session): “Classical local bifurcations of dynamical systems.” Role: Main speaker/lecturer (invited)
• II International Conference on Applied Mathematics, Colombia, September 2014.
Presented (plenary session): “Graph dynamical systems: a tool for modeling discrete processes.” Role: Main speaker/lecturer (invited)

University Seminars

• University of Catilla-La Mancha, June 2000.
Presented: “An Introduction to Dynamical Systems and Bifurcations”
• University of Murcia, November 2001.
Presented: “Open problems on bifurcation theory”
• University Jaume I of Castellon, November 2003.
Presented: “Researching on Dynamical Systems at the University of Castilla-La Mancha”
• University of Macerata, Italy, February, 2005.
Presented: “Bifurcations of dynamical systems: some examples in Economics”
• University of Urbino, Italy, November, 2006.
Presented: “Facility location in networks I”
• University of Urbino, Italy, November, 2007.
Presented: “Facility location in networks II”
• University of Catilla-La Mancha, March 2007.
Presented: “Internet Accessibility”
• Polytechnic University of Cartagena, May, 2008.
Presented: “Analysis of non-standard conditions which produce local bifurcations”
• University of Punta Arenas, Chile, September 2008.
Presented: “Networks Optimization”
• University of Murcia, May 2009.
Presented: “Dynamical systems in computations”
• University of Murcia, May 2010.
Presented: “Petri Nets as an especial type of discrete dynamical systems”
• University of Urbino, Italy, June, 2010.
Presented: “Free software for Mathematics in Engineering”
• University of Lisbon, Portugal, July, 2014.
Presented: “Higher order conditions for non-standard local bifurcations of dynamical systems”

International Conferences

• III Iberoamerican Conference on Topology and its Applications, April 1999.
Presented: “Topological Conjugations of Normal Forms in Bifurcations”
• III Italian-Spanish Conference on Topology and its Applications, June 2000.
Presented: “Topological Normal Forms of Higher Degree for the Simplest Local Bifurcations”
• 3rd European Congress of Mathematics, July 2000.
Presented: “Structural Stability under Conditions of Non-Hyperbolicity”
• European Conference on Iteration Theory, September 2000
Presented: “Simplest Normal Forms of Neimark-Sacker Bifurcations”
• IV Iberoamerican Conference on Topology and its Applications, April 2001.
Presented: “Topological Conjugations Including Higher Order Terms”
• International Conference on Computational and Mathematical Methods in Sciences and Engineering, September 2002.
Presented: “Symbolic Mathematical Computing of Bifurcations in Dynamical Systems”
• International Conference on Computational and Mathematical Methods in Sciences and Engineering, September 2002.
Presented: “Stability of Continuous Systems by Routh-Hurwitz and Mathematica”
• V Iberoamerican Conference on Topology and its Applications, June 2003.
Presented: “Topological Normal Forms of Higher Order for the Chenciner Bifurcation”
• European Conference on Iteration Theory, September 2006
Presented: “Chenciner bifurcation: some results on diffeomorphic systems”
• VII Iberoamerican Conference on Topology and its Applications, June 2008.
Presented: “Near a local topological equivalence when a quasi-center like point appears”
• International Conference on Engineering and Mathematics, July 2008
Presented: “New trends in Mathematics for Engineering based on computer/network assisted methods”

JCR-Journal Refereeing

• IEEE Transactions on Cybernetics
• Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
• Open Physics
• International Journal of Computer Mathematics
• Journal of Computational Methods in Sciences and Engineering
• Entropy
• Discrete Mathematics & Theoretical Computer Science,
• Plos One
• Applied Sciences
• Advances in Geometry,
• Chaos, Solitons & Fractals,
• Applied Bionics and Biomechanics
• Epidemiology and Infection,
• Neural Computing and Applications,
• Mathematical Methods in the Applied Sciences,
• Journal of Biological Systems,
• Acta Biotheoretica,
• Applied Mathematics & Information Sciences,
• Nonlinear Analysis Series B: Real World Applications,
• International Journal of Computer Mathematics,
• Computers & Mathematics with Applications,
• Applied Mathematics and Computation,
• Applied Mathematical Letters,