Dr Kwok Wai CHUNG (宗国威) PhD – The University of York, UK
Associate Professor

Contact Information Office: Y6509 Academic 1
Phone: +852 3442-8671
Fax: +852 3442-0250
Email: makchung@cityu.edu.hk

Research Interests Dynamical system
Nonlinear dynamics
Limit cycles
Bifurcation
Chaos
Generation of symmetrical patterns


Dr Kwok Wai Chung's research interests include dynamical systems, nonlinear dynamics, limit cycles, bifurcation and chaos, generation of symmetrical patterns. He received his PhD from the University of York (UK) in 1989. He is currently the major leader of BSc in Computing Mathematics.
Publications International Journal Papers (I) Papers on computer generation of symmetrical patterns Chung, K. W. and Chan, H. S. Y., Symmetrical Pattern from Dynamics, Computer Graphics Forum, 12(1), 33–40, 1993.
Chung, K. W. and Chan, H. S. Y., Spherical Symmetries from Dynamics, Computers & Mathematics with Applications, 29(7), 67–81, 1995.
Chung, K. W., Chan, H. S. Y. and Wang, B. N., Hyperbolic Symmetries from Dynamics, Computers & Mathematics with Applications, 31(2), 33–47, 1996.
Chung, K. W., Chan, H. S. Y. and Wang, B. N., Tessellations with the Modular Group from Dynamics, Computers and Graphics, 21(4), 523–534, 1997.
Chung, K. W., Chan, H. S. Y. and Wang, B. N., "Small and Smaller" from Dynamics, Computers and Graphics, 22(4), 527–536, 1998.
Chung, K. W., Chan, H. S. Y. and Wang, B. N., Spiral Tilings with Colour Symmetry from Dynamics, Computers & Graphics, 23(3), 439–448, 1999.
Chung, K. W., Chan, H. S. Y. and Chen, N., General Mandelbrot Sets and Julia Sets with Colour Symmetry from Equivariant Mappings of the Modular Group, Computer & Graphics, 24(6) 911–918, 2000.
Chung, K. W., Chan, H. S. Y. and Wang, B. N., Tessellations in Three-dimensional Hyperbolic Space from Dynamics and the Quaternions, Chaos, Solitons & Fractals, 12, 1181–97, 2001.
Chung, K. W., Chan, H. S. Y. and Wang, B. N., Tessellations with Symmetries of the Wallpaper Groups and the Modular Group in the Hyperbolic 3-Space from Dynamics, Computers & Graphics, 25(2), 333–341, 2001.
Chung, K. W., Chan, H. S. Y. and Wang, B. N., Efficient Generation of Hyperbolic Symmetries from Dynamics, Chaos, Solitons and Fractals, 13(6), 1175–90, 2002.
Chen, N., Zhu, X. L. and Chung, K. W., M and J sets from Newton's Transformation of the Transcendental Mapping F(z) = e^z^w + c with VCPS, Computer & Graphics, 26(2), 371–383, 2002.
Chung, K. W. and Wang, B. N., Tessellations with Symmetries of the Triangle Groups from Dynamics, International Journal of Bifurcation and Chaos, 13(11), 3505–3518, 2003.
Chung, K. W., Chan, H. S. Y. and Wang, B. N., Automatic Generation of Nonperiodic Patterns from Dynamical Systems, Chaos, Solitons and Fractals, 19(5), 1177–1187, 2004.
Chung, K. W. and Wang, B. N., Automatic Generation of Aesthetic Patterns on Aperiodic Tilings by Means of Dynamical Systems, International Journal of Bifurcation and Chaos, 14(9), 3249–3267, 2004.
Chung, K. W. and Ma, H. M., Automatic Generation of Aesthetic Patterns on Fractal Tilings by Means of Dynamical Systems, Chaos, Solitons and Fractals, 24(4), 1145–1158, 2005.
Ouyang, P C and Chung, K. W., Beautiful Math, Part 3: Hyperbolic Aesthetic Patterns Based on Conformal Mappings, IEEE Computer Graphics and Applications, 34(2), 72-79, 2014.
Chen, N, Zhang, Y T and Chung, K W, Construction of Aesthetic Spherical Patterns from Planar IFSs, Fractals, 24, 1650030, 2016.
Chen, N and Chung, K W, Efficient Generation of Hyperbolic Patterns from a Single Asymmetric Motif, Fractals, 24, 1650043, 2016.
Ouyang, P C, Tang X S, Chung, K W and Yu T, Fractal Tilings based on Successive Adjacent Substitution Rule, Complexity, Article ID 6451921, 2018.
Chen, N, Chen, Y N and Chung, K W, Fractals from Nonlinear IFSs of the Complex Mapping Family f (z) =z^n + c , Fractals, 26, 1850044, 2018.
Ouyang, P C, Tang X S, Chung, K W and Yu T, Spiral Patterns of Color Symmetry from Dynamics, Nonlinear Dynamics, 94(1), 261-272, 2018.
Ouyang, P C, Fathauer, R W, Chung, K W and Wang X C, Automatic generation of hyperbolic drawings, Applied Mathematics and Computation, 347, 653-663, 2019.
Wang, X C, Ouyang, P C, Chung, K W, Zhan, X G, Yi, H and Tang, X S, Fractal tilings from substitution tilings , Fractals, 27(2), 1950009, 2019.
Wang, X C, Yu, T, Chung, K W, Gdawiec, K and Ouyang, P C, Stereographic Visualization of 5-Dimensional Regular Polytopes, Symmetry, 11(3), 391, 2019.
(II) Papers on nonlinear dynamics and limit cycles Chan, H. S. Y., Chung, K. W. and Xu, Z., A Perturbation-iterative Method for Determining Limit Cycles of Strongly Non-linear Oscillators, Journal of Sound and Vibration, 183(4), 707–717, 1995.
Chan, H. S. Y., Chung, K. W. and Xu, Z., A Perturbation-incremental Method for Strongly Non-linear Oscillators, Int. Journal of Non-Linear Mechanics, 31(1), 59–72, 1996.
Xu, Z., Chan, H. S. Y. and Chung, K. W., Separatrices and Limit Cycles of Strongly Nonlinear Oscillators by the Perturbation-Incremental Method, Nonlinear Dynamics, 11, 213–233, 1996.
Chan, H. S. Y., Chung, K. W. and Xu, Z., Stability and Bifurcations of Limit Cycles by the Perturbation-incremental Method, Journal of Sound and Vibration, 206(4), 589–604, 1997.
Chan, H. S. Y., Chung, K. W. and Qi, D. W., Bifurcating Limit Cycles in Quadratic Polynomial Differential Systems, Physica A, 288, 417–423, 2000.
Chan, H. S. Y., Chung, K. W. and Qi, D. W., Some Bifurcation Diagrams for Limit Cycles of Quadratic Differential Systems, International Journal of Bifurcation and Chaos, 11(1), 197–206, 2001.
Chan, H. S. Y., Chung, K. W. and Li, J. B., Bifurcations of Limit Cycles in Z₃-Equivariant Planar Vector Field of Degree 5, International Journal of Bifurcation and Chaos, 11, 2287–2298, 2001.
Li, J. B., Chan, H. S. Y. and Chung, K. W., Bifurcations of Limit Cycles in Z₆-Equivariant Planar Vector Fields of Degree 5, Science in China (Series A), 45(7), 817–826, 2002.
Li, J. B., Chan, H. S. Y. and Chung, K. W., Investigations of Bifurcations of Limit Cycles in Z₂-Equivariant Planar Vector Field of Degree 5, International Journal of Bifurcation and Chaos, 12(10), 2137–2157, 2002.
Chung, K. W., Chan, C. L., Xu, Z. and Mahmoud, G. M., A perturbation-Incremental Method for Strongly Nonlinear Autonomous Oscillators with Many Degrees of Freedom, Nonlinear Dynamics, 28(3), 243–259, 2002.
Xu, J. and Chung, K. W., Effects of time delayed position feedback on a van der Pol-Duffing oscillator, Physica D, 180(1), 17–39, 2003.
Chung, K. W., Chan, C. L. and Xu, J., An Efficient Method for Switching Branches of Period-doubling Bifurcations of Strongly Non-linear Autonomous Oscillators with Many Degrees of Freedom, Journal of Sound and Vibration, 267(4), 787–808, 2003.
Li, J. B., Chan, H. S. Y. and Chung, K. W., Some Lower Bounds for H(n) in Hilbert's 16th Problem, Qualitative Theory of Dynamical Systems, 3, 345–360, 2003.
Xu, J., Chung, K. W. and Chan, H. S. Y., Co-dimension 2 bifurcations and chaos in cantilevered pipe conveying time varying fluid with three-to-one internal resonances, Acta Mechanica Solida Sinica, 16(3), 245–255, 2003.
Xu, J. and Chung, K. W., Delay reduced double Hopf bifurcation in a limit cycle oscillator: extension of a perturbation-incremental method, Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications & Algorithms, 11a, 136–143, 2004.
Chung, K. W., Chan, C. L., Xu, Z. and Xu, J., A perturbation-incremental method for strongly nonlinear non-autonomous oscillators, International Journal of Non-Linear Mechanics, 40(6), 845–859, 2005.
Lee, B. H. K., Liu, L. and Chung, K. W., Airfoil motion in subsonic flow with strong cubic nonlinear restoring forces, Journal of Sound and Vibration, 281(3–5), 699–717, 2005.
Liu, Z. R. and Chung, K. W., Hybrid control of bifurcation in continuous nonlinear dynamical systems, International Journal of Bifurcation and Chaos, 15(12), 3895–3903, 2005.
Chung, K. W., Chan, C. L. and Xu, J., A perturbation-incremental method for delay differential equations, International Journal of Bifurcation and Chaos, 16(9), 2529–2544, 2006.
Xu, J., Chung, K. W. and Chan, C. L., An efficient method for studying weak resonant double Hopf bifurcation in nonlinear systems with delayed feedbacks, SIAM Journal of Applied Dynamical Systems, 6(1), 29–60, 2007.
Chung, K. W. and Yuan, X. P., Existence and stability of quasi-periodic breathers in networks of Ginzburg-Landau oscillators, Physica D, 227, 43–50, 2007.
Chung, K. W., Chan, C. L. and Lee, B. H. K., Bifurcation analysis of a two-degree-of-freedom aeroelastic system with freeplay structural nonlinearity by a perturbation-incremental method, Journal of Sound and Vibration, 299(3), 520–539, 2007.
Chung, K. W. and Yuan, X. P., Periodic and quasi-periodic solutions for the complex Ginzburg-Landau equation, Nonlinearity, 21, 435–451, 2008.
Chung, K. W., He, Y. B. and Lee, B. H. K., Bifurcation analysis of a two-degree-of-freedom aeroelastic system with hysteresis structural nonlinearity by a perturbation-incremental method, Journal of Sound and Vibration, 320, 163–183, 2009.
Xu, J. and Chung, K. W., Dynamics for a class of nonlinear systems with time delay, Chaos, Solitons and Fractals, 40, 28–49, 2009.
Xu, J. and Chung, K. W., A perturbation-incremental scheme for studying Hopf bifurcation in delayed differential systems, Science in China Series E, 52(3), 1–11,2009.
Xu, J. and Chung, K. W., Double Hopf bifurcation with strong resonances in delayed systems with nonlinearities, Mathematical Problems in Engineering, Art. ID 759363, 2009.
Xu, J., Chung, K. W. and Zhao, Y. Y., Delayed saturation controller to vibration suppression in a stainless-steel beam, Nonlinear Dynamics, 62, 177–193, 2010.
Cao, Y. Y., Chung, K. W. and Xu, J., A novel construction of homoclinic and heteroclinic orbits in nonlinear oscillators by a Perturbation-incremental method, Nonlinear Dynamics, 64, 221-236, 2011..
Chung, K. W., Ng, K. T. and Dai, H.-H., Bifurcations in a boundary-value problem of a nonlinear model for stress-induced phase transitions, International Journal of Bifurcation and Chaos, 21, 3231-3247, 2011.
Chung, K. W. and Liu, Z. H., Nonlinear analysis of chatter vibration in a cylindrical transverse grinding process with two time delays using a nonlinear time transformation method, Nonlinear Dynamics, 66, 441-456, 2011.
Chung, K. W. and Cao, Y. Y., Exact front, soliton and hole solutions for a modified complex Ginzburg-Landau equation from harmonic balance method, Applied Mathematics and Computation, 218, 5140-5145, 2012.
Wang, H L and Chung, K W, Analytical solutions of a generalized Duffing-harmonic oscillator by a nonlinear time transformation method, Physics Letters A, 376, 1118-1124, 2012.
Cao, Y Y and Chung, K W, Computation of stationary pulse solutions of the cubic-quintic complex Ginzburg-Landau equation by a perturbation-incremental method, International Journal of Numerical Analysis and Modeling, Series B, 3, 429-441, 2012.
Zhang, S, Chung, K W and Xu, J, Stability switch boundaries in an internet congestion control model with diverse time delays, International Journal of Bifurcation and Chaos, 23, 1330016, 2013.
Hu, K and Chung, K W, On the stability analysis of a pair of van der Pol oscillators with delayed self-connection, position and velocity couplings AIP Advances, 3, 112118, 2013.
Chung, K W, Cao, Y Y, Fahsi, A and Belhaq, M, Analytical approximation of heteroclinic bifurcations in 1:4 resonance using a nonlinear transformation method, Nonlinear Dynamics, 78, 2479-2486, 2014.
Chen, Y L, Chung, K W, Xu, J and Sun Y X, Analysis of vibration suppression of master structure in nonlinear systems using nonlinear delayed absorber, International Journal of Dynamics and Control, 2, 55-67, 2014.
Zhang, S, Xu, J and Chung, K W, On the stability and multi-stability of a TCP/RED congestion control model with state-dependent delay and discontinuous marking function, Communications in Nonlinear Science and Numerical Simulation, 23, 269-284, 2015.
Xu, J, Chen Y L, Chung, K W, An improved time-delay saturation controller for suppression of nonlinear beam vibration, Nonlinear Dynamics, 82, 1691-1707, 2015.
Qin, B W, Chung, K W, Fahsi, A and Belhaq, M, On the heteroclinic connections in the 1:3 resonance problem, International Journal of Bifurcation and Chaos, 26, 1650143, 2016.
Chung, K W and Lui, R, Dynamics of two-strain influenza model with cross-immunity and no quarantine class, Journal of Mathematical Biology, 73, 1467-1489, 2016.
Liu, Z H, Hu, K and Chung, K W, Nonlinear analysis of a closed-loop tractor-semitrailer vehicle system with time delay, Mechanical Systems and Signal Processing, 76-77, 696-711, 2016.
Zhang, S, Xu, J and Chung, K W, Desynchronization-based congestion suppression for a star-type Internet system with arbitrary dimension, Neurocomputing, 266, 42–55, 2017.
Qin, B W, Chung, K W, Rodríguez-Luis, A J and Belhaq, M, Homoclinic-doubling and homoclinic-gluing bifurcations in the Takens-Bogdanov normal form with D4 symmetry, Chaos, 28, 093107, 2018.
Zhou, Y, Wang, Z and Chung, K W, Turning Motion Control Design of a Two-Wheeled Inverted Pendulum Using Curvature Tracking and Optimal Control Theory, Journal of Optimization Theory and Applications, 181(2), 634-652, 2019.
Algaba, A, Chung, K W, Qin, B W and Rodríguez-Luis, A J, Revisiting the analysis of a codimension-three Takens–Bogdanov bifurcation in planar reversible systems, Nonlinear Dynamics, 96(4), 2567-2580, 2019.
Algaba, A, Chung, K W, Qin, B W, Rodríguez-Luis, A J, A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens–Bogdanov normal form, Nonlinear Dynamics, 97(2), 979-990, 2019.
Bellizzi, S, Chung, K W and Sampaio, R, Response regimes of a linear oscillator with a nonlinear energy sink involving an active damper with delay, Nonlinear Dynamics, 97(2), 1667-1684, 2019.
Algaba, A, Chung, K W, Qin, B W, Rodríguez-Luis, A J, Computation of all the coefficients for the global connections in the Z2-symmetric Takens-Bogdanov normal forms, Communications in Nonlinear Science and Numerical Simulation, 81,105012, 2020.
Qin, B W, Chung, K W, Algaba, A, Rodríguez-Luis, A J, Analytical approximation of cuspidal loops using a nonlinear time transformation method, Applied Mathematics and Computation, 373, 125042, 2020.
Qin, B W, Chung, K W, Algaba, A, Rodríguez-Luis, A J, High-order analysis of global bifurcations in a codimension-three Takens-Bogdanov singularity in reversible systems. International Journal of Bifurcation and Chaos, 30(1), 2050017, 2020. (Appendices A - E)
Qin, B W, Chung, K W, Algaba, A, Rodríguez-Luis, A J, High-order analysis of canard explosion in the Brusselator equations, to appear in International Journal of Bifurcation and Chaos.
Algaba, A, Chung, K W, Qin, B W, Rodríguez-Luis, A J, Analytical approximation of the canard explosion in a van der Pol system with the nonlinear time transformation method, to appear in Physica D.
Qin, B W, Chung, K W, Algaba, A, Rodríguez-Luis, A J, High-order study of the canard explosion in an aircraft ground dynamics model, accepted for publication in Nonlinear Dynamics.
(III) Paper on Mathematical Ecology Liu, J. G., Chung, K. W. and Chan, H. S. Y., An Ordinary Differential Equation Model of Succession of Korean Pine Broadleaf Forest, Journal of Biological Systems, 5(3), 375–388, 1997.
Yu, S. X., Chung, K. W., Chan, H. S. Y., Zang, R. G. and Yang, Y. C., Comparison of Ecological Entropy with Random and Systematic Sampling, Acta Phytoecologica Sinica, 22(5), 473–480, 1998 (in Chinese).
Yu, S. X., Chan, H. S. Y. and Chung, K. W., A Comparison of Sampling Designs in a Hainan Tropical Rain Forest, Community Ecology, 1(1), 81–87, 2000.
(IV) Others Chung, K. W. and Sudbery A., Octonions and the Lorentz and Conformal Groups of Ten-dimensional Space-time, Physics Letters B, 198, 161–164, 1987.
Lam J. and Chung, K. W., Error Bounds for Padé Approximations of e-z on the Imaginary Axis, Journal of Approximation Theory, 69, 222–230, 1992.
Lam, J., Li, Z., Wei, Y. M., Feng, J. E. and Chung, K. W., Estimates of the spectral condition number, Linear and Multilinear Algebra, 59 (3), 249-260, 2011.
Conference Papers Chan, H. S. Y., Chung, K. W. and Xu Z., Calculation of Limit Cycles, ICNM-III, Shanghai, P. R. China, 597–601, 1998.
Chan, H. S. Y., Chung, K. W. and Li, J. B., Bifurcations of Limit Cycles in Z_q-Equivariant Planar Vector Fields of Degree 5, in Proceeding of the International Conference on Foundations of Computational Mathematics in honor of Professor Steve Smale's 70th Birthday, 61–83, 2002.
Xu, J., Chung, K. W., Ge, J. H. and Huang, Y., Delay-induced Hopf Bifurcation and periodic solution in a BAM network with two delays, the proceedings of the 19th International Conference on Artificial Neural Networks (ICANN 2009), C. Alippi et al. (Eds.), Cyprus, Part II, LNCS 5769, 534–543, 2009.
Bellizzi, S, Chung, K W and Hu, K, Vibration absorption with a nonlinear absorber including time delay, in the Second International Conference on Structural Nonlinear Dynamics and Diagnosis (CSNDD 2014), Agadir, Morocco, May 2014.
Bellizzi, S and Chung, K W, Vibration reduction using a nonlinear attachment including an active damper with delay, Proceedings of the ASME International Mechanical Engineering Congress and Exposition (IMECE 2015), American Society of Mechanical Engineers, Vol. 4B – 2015.
Liu, Z, Chung, K W and Wang, W, A perturbed nonlinear model of an articulated vehicle with driver control, CHAOS 2017 - Proceedings: 10th Chaotic Modeling and Simulation International Conference, pp. 549-558, 2017.
Symmetrical Patterns The following aesthetic patterns are generated by using equivariant and invariant mappings. For detailed construction of the mappings for the creation of exotic patterns, please see the papers on automatic generation of symmetrical patterns.
Fractal tilings





Hyperbolic symmetry-2D





Hyperbolic symmetry-3D





Penrose tilings





Smaller and smaller





Spherical symmetry





Spiral symmetry





Symmetry of the modular group





Wallpaper symmetry





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