Marius Florin Danca

Publications

• Selected publications
• Convergence of a parameter switching algorithm for a class of nonlinear continuous systems and a generalization of Parrondo’s paradox

  M. - F. Danca. (2013)

  Communications in Nonlinear Science and Numerical Simulation, 18(3), 500–510.
• 2022
• Symmetry-breaking and bifurcation diagrams of fractional-order maps

  M. - F. Danca. (2022)

  Communications in Nonlinear Science and Numerical Simulation, 116, 106760.
• Caputo delta weakly fractional difference equations

  M. Feckan, M. Pospisil, M. - F. Danca, & J. Wang. (2022)

  Fractional Calculus and Applied Analysis, September.
• Fractional order logistic map: Numerical approach

  M. - F. Danca. (2022)

  Chaos, Solitons & Fractals, 157, 111851.
• D3 Dihedral Logistic Map of Fractional Order

  M. - F. Danca, & N. Kuznetsov. (2022)

  Mathematics, 10(213).
• 2021
• Hopfield Neuronal Network of Fractional Order: A note on its numerical integration

  M. - F. Danca. (2021)

  Chaos, Solitons & Fractals, 151(111219).
• Coexisting Hidden and self-excited attractors in an economic system of integer or fractional order

  M. - F. Danca. (2021)

  International Journal of Bifurcation and Chaos, 31(4), 2150062.
• Hidden Strange Nonchaotic Attractors

  M. - F. Danca, & N. Kuznetsov. (2021)

  Mathematics, 9(6), 652.
• Attractor as a convex combination of a set of attractors

  M. - F. Danca, M. Feckan, N. Kuznetsov, & G. Chen. (2021)

  Communications in Nonlinear Science and Numerical Simulation, 96, 105721.
• Hidden and self-exited attractors in a heterogeneous Cournot oligopoly model

  M. - F. Danca, & M. Lampart. (2021)

  Chaos, Solitons & Fractals, 142, 110371.
• Coupled Discrete Fractional-Order Logistic Maps

  M. - F. Danca, M. Feckan, N. Kuznetsov, & G. Chen. (2021)

  Mathematics, 9(18), 2204.
• Matlab code for Lyapunov exponents of fractional-order systems, Part II: The non-commensurate case

  M. - F. Danca. (2021)

  International Journal of Bifurcation and Chaos, 31(12), 2150187.
• 2020
• Puu system of fractional order and its chaos suppression

  M. - F. Danca. (2020)

  Symmetry, 12(3), 340.
• Chaos suppression in a Gompertz-like discrete system of fractional order

  M. - F. Danca, & M. Feckan. (2020)

  International Journal of Bifurcation and Chaos, 30(3), 2050049.
• Bifurcation and Chaos in Fractional- Order Systems

  Bifurcation and Chaos in Fractional- Order Systems. (2020)

  (M. - F. Danca & G. Chen, Eds.) (ISBN 978-3-0365-0093-5 (PDF).)Basel: MDPI.
• 2019
• Graphical structure of attraction basins of hidden attractors: the Rabinovich-Fabrikant system

  M. - F. Danca, P. Bourke, & N. Kuznetsov. (2019)

  International Journal of Bifurcation and Chaos, 29(1), 1930001.
• Difference equations with impulses

  M. - F. Danca, & M. Feckan. (2019)

  Opuscula Mathematica, 39(1), 5-22.
• Chaos control in the fractional order logistic map via impulses

  M. - F. Danca, M. Feckan, & N. Kuznetsov. (2019)

  Nonlinear Dynamics, 98(2), 1219–1230.
• Rich dynamics and anticontrol of extinction in a prey-predator system

  M. - F. Danca, M. Feckan, N. Kuznetsov, & G. Chen. (2019)

  Nonlinear Dynamics, 98(2), 1421–1445.
• Hidden chaotic attractors and chaos suppression in an impulsive discrete economical supply and demand dynamical system

  M. - F. Danca, & M. Feckan. (2019)

  Communications in Nonlinear Science and Numerical Simulation, 74( ), 1-13.
• 2018
• Matlab code for Lyapunov exponents of fractional order systems

  M. - F. Danca, & N. Kuznetsov. (2018)

  International Journal of Bifurcation and Chaos, 28(5), 1850067.
• Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system

  M. - F. Danca, M. Feckan, & G. Chen. (2018)

  Nonlinear Dynamics, 91(4), 2523–2540.
• Generalization of the Filippov method for systems with large periodic input

  C. Morel, & M. - F. Danca. (2018)

  Mathematics and Computers in Simulation, 146, 1-13.
• Fractional-order PWC systems without zero Lyapunov exponents

  M. - F. Danca, N. Kuznetsov, & G. Chen. (2018)

  Nonlinear Dynamics, 92(3), 1061–1078.
• Approximating hidden chaotic attractors via parameter switching

  M. - F. Danca, & N. Kuznetsov. (2018)

  CHAOS, 28, 013127.
• Lyapunov exponents of a hyperchaotic discontinuous 4D system of integer or fractional order

  M. - F. Danca. (2018)

  Entropy, 20, 337.
• 2017
• Impulsive stabilization of chaos in fractional-order systems

  M. - F. Danca, M. Fečkan, & G. Chen. (2017)

  Nonlinear Dynamics, 89(3), 1889–1903.
• Unusual dynamics and hidden attractors of the Rabinovich–Fabrikant system

  M. - F. Danca, N. Kuznetsov, & G. Chen. (2017)

  Nonlinear Dynamics, 88(1), 791–805.
• Hidden chaotic attractors in fractional-order systems

  M. - F. Danca. (2017)

  Nonlinear Dynamics, 89(1), 577–586.
• Hidden chaotic attractors in fractional-order systems

  M. - F. Danca. (2017)

  Nonlinear Dynamics, 89(1), 577–586.
• Impulsive stabilization of chaos in fractional-order systems

  M. - F. Danca, M. Feckan, & G. Chen. (2017)

  Nonlinear Dynamics, 89(3), 1889–1903.
• On the numerical integration of discontinuous dynamical systems

  M. - F. Danca, & M. Feckan. (2017)

  International Journal of Bifurcation and Chaos, 27(14), 1750218.
• Parameter Switching Synchronization

  M. - F. Danca, & N. Kuznetsov. (2017)

  Applied Mathematics and Computation, 313, 94-102.
• 2016
• Note on a parameter switching method for nonlinear ODEs

  M. - F. Danca, & M. Fečkan. (2016)

  Mathematica Slovaca, 66(2).
• Hidden transient chaotic attractors of Rabinovich–Fabrikant system

  M. - F. Danca. (2016)

  Nonlinear Dynamics, 86(2), 1263–1270.
• Emulating “Chaos + Chaos = Order” in Chen’s Circuit of Fractional Order by Parameter Switching

  W. K. S. Tang, & M. - F. Danca. (2016)

  International Journal of Bifurcation and Chaos, 26(06), 1650096.
• Chaos control of Hastings–Powell model by combining chaotic motions

  M. - F. Danca, & J. Chattopadhyay. (2016)

  Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(4), 043106.
• Hidden and Nonstandard Bifurcation Diagram of an Alternate Quadratic System

  G. Pastor, M. Romera, M. - F. Danca, A. Martin, A. B. Orue, F. Montoya, & L. H. Encinas. (2016)

  International Journal of Bifurcation and Chaos, 26(02), 1650036.
• Looking More Closely at the Rabinovich–Fabrikant System

  M. - F. Danca, M. Fec̆kan, N. Kuznetsov, & G. Chen. (2016)

  International Journal of Bifurcation and Chaos, 26(02), 1650038.
• Suppressing chaos in a simplest autonomous memristor-based circuit of fractional order by periodic impulses

  M. - F. Danca, W. K. S. Tang, & G. Chen. (2016)

  Chaos, Solitons & Fractals, 84(C), 31–40.
• Parrondo’s paradox for chaos control and anticontrol of fractional-order systems

  M. - F. Danca, & W. K. S. Tang. (2016)

  Chinese Physics B, 25(1), 010505.
• Chaos Control and Anticontrol of Complex Systems via Parrondo’s Game

  M. - F. Danca. (2016)

  In J. Lü, X. Yu, G. Chen, & W. Yu (Eds.), Complex Systems and Networks (p. 263–282)Berlin, Heidelberg: Springer Berlin Heidelberg.
• 2015
• Continuous Approximations of a Class of Piecewise Continuous Systems

  M. - F. Danca. (2015)

  International Journal of Bifurcation and Chaos, 25(11), 1550146.
• A new piecewise linear Chen system of fractional-order: Numerical approximation of stable attractors

  M. - F. Danca, M. A. Aziz-Alaoui, & M. Small. (2015)

  Chinese Physics B, 24(6), 060507.
• Lyapunov exponents of a class of piecewise continuous systems of fractional order

  M. - F. Danca. (2015)

  Nonlinear Dynamics, 81(1-2), 227–237.
• Breaking Points in Quartic Maps

  M. Romera, G. Pastor, A. Martin, A. B. Orue, F. Montoya, & M. - F. Danca. (2015)

  International Journal of Bifurcation and Chaos, 25(04), 1550051.
• Suppressing chaos in discontinuous systems of fractional order by active control

  M. - F. Danca, & R. Garrappa. (2015)

  Applied Mathematics and Computation, 257(C), 89–102.
• 2014
• Noise induced complexity: patterns and collective phenomena in a small-world neuronal network

  Y. Zheng, Q. Wang, & M. - F. Danca. (2014)

  Cognitive Neurodynamics, 8(2), 143–149.
• Generalized Form of Parrondo's Paradoxical Game with Applications to Chaos Control

  M. - F. Danca, M. Fečkan, & M. Romera. (2014)

  International Journal of Bifurcation and Chaos, 24(01), 1450008.
• Synchronization of piecewise continuous systems of fractional order

  M. - F. Danca. (2014)

  Nonlinear Dynamics, 78(3), 2065–2084.
• 2013
• Parameter switching in a generalized Duffing system: Finding the stable attractors

  M. - F. Danca, & N. Lung. (2013)

  Applied Mathematics and Computation, 223(C), 101–114.
• Suppressing chaos in fractional-order systems by periodic perturbations on system variables

  M. - F. Danca, W. K. S. Tang, Q. Wang, & G. Chen. (2013)

  European Physical Journal B, 86(3).
• Graphical exploration of the connectivity sets of alternated Julia sets: M, the set of disconnected alternated Julia sets

  M. - F. Danca, P. Bourke, & M. Romera. (2013)

  Nonlinear Dynamics, 73(1-2), 1155–1163.
• A Method to Solve the Limitations in Drawing External Rays of the Mandelbrot Set

  M. Romera, G. Pastor, A. B. Orue, A. Martin, M. - F. Danca, & F. Montoya. (2013)

  Mathematical Problems in Engineering, 2013, 1–9.
• Sustaining stable dynamics of a fractional-order chaotic financial system by parameter switching

  M. - F. Danca, R. Garrappa, W. K. - S. Tang, & G. Chen. (2013)

  Computers & Mathematics with Applications, 66(5), 702–716.
• Convergence of a parameter switching algorithm for a class of nonlinear continuous systems and a generalization of Parrondo’s paradox

  M. - F. Danca. (2013)

  Communications in Nonlinear Science and Numerical Simulation, 18(3), 500–510.
• 2012
• Harmonic Analysis in Discrete Dynamical Systems

  G. Pastor, M. Romera, A. B. Orue, A. Martin, M. F. Danca, & F. Montoya. (2012)

  International Journal of Modern Nonlinear Theory and Application, 01(01), 14–31.
• Harmonic Analysis in Discrete Dynamical Systems

  G. Pastor, M. Romera, A. B. Orue, A. Martin, M. - F. Danca, & F. Montoya. (2012)

  International Journal of Modern Nonlinear Theory and Application, 1(1), 14-31.
• Complex dynamics of compound bursting with burst episode composed of different bursts

  Z. Yang, Q. Wang, M. - F. Danca, & J. Zhang. (2012)

  Nonlinear Dynamics, 70(3), 2003–2013.
• Finding attractors of continuous-time systems by parameter switching

  M. - F. Danca, M. Romera, G. Pastor, & F. Montoya. (2012)

  Nonlinear Dynamics, 67(4), 2317–2342.
• Modeling numerically the Rikitake's attractors by parameter switching

  M. - F. Danca, & S. Codreanu. (2012)

  Journal of the Franklin Institute, 349(3), 861–878.
• Chaos suppression via periodic pulses in a class of piece-wise continuous systems

  M. - F. Danca. (2012)

  Computers & Mathematics with Applications, 64(5), 849–855.
• OGY method for a class of discontinuous dynamical systems

  M. - F. Danca. (2012)

  Nonlinear Dynamics, 70(2), 1523–1534.
• PARRONDO'S GAME MODEL TO FIND NUMERICALLY STABLE ATTRACTORS OF A TUMOR GROWTH MODEL

  M. - F. DANCA, & D. LAI. (2012)

  International Journal of Bifurcation and Chaos, 22(10), 1250258.
• Chaos suppression via periodic change of variables in a class of discontinuous dynamical systems of fractional order

  M. - F. Danca. (2012)

  Nonlinear Dynamics, 70(1), 815–823.
• 2011
• Calculation of the Structure of a Shrub in the Mandelbrot Set

  G. Pastor, M. Romera, A. B. Orue, A. Martín, M. - F. Danca, & F. Montoya. (2011)

  Discrete Dynamics in Nature and Society, 2011, 1–23.
• Numerical approximation of a class of discontinuous systems of fractional order

  M. - F. Danca. (2011)

  Nonlinear Dynamics, 66(1-2), 133–139.
• APPROACH OF A CLASS OF DISCONTINUOUS DYNAMICAL SYSTEMS OF FRACTIONAL ORDER: EXISTENCE OF SOLUTIONS

  M. - F. DANCA. (2011)

  International Journal of Bifurcation and Chaos, 21(11), 3273–3276.
• SYNTHESIZING THE LÜ ATTRACTOR BY PARAMETER-SWITCHING

  M. - F. DANCA. (2011)

  International Journal of Bifurcation and Chaos, 21(01), 323–331.
• Attractors synthesis of a class of networks

  M. - F. Danca, & C. Morel. (2011)

  Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, 18(5), 601–614.
• 2010
• An averaging model for chaotic system with periodic time-varying parameter

  Y. Mao, W. K. S. Tang, & M. - F. Danca. (2010)

  Applied Mathematics and Computation, 217(1), 355–362.
• Finding stable attractors of a class of dissipative dynamical systems by numerical parameter switching

  M. - F. Danca. (2010)

  Dynamical Systems, 25(2), 189–201.
• Synthesizing attractors of Hindmarsh–Rose neuronal systems

  M. - F. Danca, & Q. Wang. (2010)

  Nonlinear Dynamics, 62(1-2), 437–446.
• Fractional-order attractors synthesis via parameter switchings

  M. F. Danca, & K. Diethelm. (2010)

  Communications in Nonlinear Science and Numerical Simulation, 15(12), 3745–3753.
• Chaotic behavior of a class of discontinuous dynamical systems of fractional-order

  M. - F. Danca. (2010)

  Nonlinear Dynamics, 60(4), 525–534.
• Attractors synthesis for a Lotka–Volterra like system

  M. - F. Danca. (2010)

  Applied Mathematics and Computation, 216(7), 2107–2117.
• Dibujo de los rayos externos de Douady y Hubbard

  G. Pastor, M. Romera, A. B. Orue, A. Martín, M. F. Danca, & F. Montoya. (2010)

  In NoLineal 2010 (p. 110).
• On the uniqueness of solutions to a class of discontinuous dynamical systems

  M. F. Danca. (2010)

  Nonlinear Analysis: Real World Applications, 11(3), 1402–1412.
• Dendritas de Misiurewicz en el conjunto de Mandelbrot

  A. Martín, G. Pastor, M. Romera, A. B. Orue, M. F. Danca, & F. Montoya. (2010)

  In NoLineal 2010 (p. 108).
• 2009
• ALTERNATED JULIA SETS AND CONNECTIVITY PROPERTIES

  M. - F. DANCA, M. ROMERA, & G. PASTOR. (2009)

  International Journal of Bifurcation and Chaos, 19(06), 2123–2129.
• 2008
• Fractal and statistical analysis on digits of irrational numbers

  D. Lai, & M. - F. Danca. (2008)

  Chaos, Solitons & Fractals, 36(2), 246–252.
• Random parameter-switching synthesis of a class of hyperbolic attractors

  M. - F. Danca. (2008)

  Chaos: An Interdisciplinary Journal of Nonlinear Science, 18(3), 033111.
• A switching scheme for synthesizing attractors of dissipative chaotic systems

  M. - F. Danca, W. K. S. Tang, & G. Chen. (2008)

  Applied Mathematics and Computation, 201(1-2), 650–667.
• Numerical approximations of a class of switch dynamical systems

  M. - F. Danca. (2008)

  Chaos, Solitons & Fractals, 38(1), 184–191.
• 2007
• ON A DYNAMICAL SYSTEM WITH MULTIPLE CHAOTIC ATTRACTORS

  X. LUO, M. SMALL, M. - F. DANCA, & G. CHEN. (2007)

  International Journal of Bifurcation and Chaos, 17(09), 3235–3251.
• Deterministic and random synthesis of discrete chaos

  M. Romera, M. Small, & M. - F. Danca. (2007)

  Applied Mathematics and Computation, 192(1), 283–297.
• On a class of non-smooth dynamical systems: a sufficient condition for smooth versus non-smooth solutions

  M. - F. Danca. (2007)

  Regular and Chaotic Dynamics, 12(1), 1–11.
• 2004
• Controlling chaos in discontinuous dynamical systems

  M. - F. Danca. (2004)

  Chaos, Solitons & Fractals, 22(3), 605–612.
• BIFURCATION AND CHAOS IN A COMPLEX MODEL OF DISSIPATIVE MEDIUM

  M. - F. DANCA, & G. CHEN. (2004)

  International Journal of Bifurcation and Chaos, 14(10), 3409–3447.
• CHAOTIFYING DISCONTINUOUS DYNAMICAL SYSTEMS VIA TIME-DELAY FEEDBACK ALGORITHM

  M. - F. DANCA. (2004)

  International Journal of Bifurcation and Chaos, 14(07), 2321–2339.
• 2002
• SYNCHRONIZATION OF SWITCH DYNAMICAL SYSTEMS

  M. - F. DANCA. (2002)

  International Journal of Bifurcation and Chaos, 12(08), 1813–1826.
• On a possible approximation of discontinuous dynamical systems

  M. - F. Danca, & S. Codreanu. (2002)

  Chaos, Solitons & Fractals, 13(4), 681–691.
• 2001
• On a class of discontinuous dynamical system

  M. - F. D. (2001)

  Miskolc Mathematical Notes, 2(1), 103-116.
• 1997
• Suppression of chaos in a one-dimensional mapping

  S. Codreanu, & M. - F. Danca. (1997)

  Journal of Biological Physics, 23(1), 1-9.
• Control of chaos in a nonlinear prey-predator model

  S. Codreanu, & M. - F. Danca. (1997)

  Polish Journal of Environmental Studies, 6(1), 21-24.
• Detailed analysis of a nonlinear prey-predator model

  M. - F. Danca, S. Codreanu, & B. Bako. (1997)

  Journal of Biological Physics, 23(1), 11-20.