RIDDLED BASINS
J.C. ALEXANDERResearch partially supported by the National Science Foundation under grant DMS-90–01788. Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA JAMES A. YORKEResearch partially supported by Air Force Office of Scientific Research grant F49620–92-J-0033 Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA ZHIPING YOUDepartment of Mathematics, University of Maryland, College Park, Maryland 20742, USA I. KANResearch partially supported by Air Force Office of Scientific Research grant F49620–92-J-0033 Department of Mathematics, George Mason University, Fairfax, Virginia 22030, USA
Received: April 20, 1992
Revised: July 24, 1992
Theory and examples of attractors with basins which are of positive measure, but contain no open sets, are developed; such basins are called riddled. A theorem is established which states that riddled basins are detected by normal Lyapunov exponents. Several examples, both mathematically rigorous and numerical, motivated by applications in the literature, are presented.
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Y. Z. Xu, Q. Ouyang, J. G. Wu, J. A. Yorke, G. X. Xu, D. F. Xu, R. D. Soloway, J. Q. Ren. (2000) Using fractal to solve the multiple minima problem in molecular mechanics calculation. Journal of Computational Chemistry 21:12, 1101-1108. Online publication date: 1-Sep-2000. [ CrossRef ]
Peter Ashwin, John R. Terry. (2000) On riddling and weak attractors. Physica D: Nonlinear Phenomena 142:1-2, 87-100. Online publication date: 1-Aug-2000. [ CrossRef ]
Tomasz Kapitaniak, Yuri Maistrenko, Svitlana Popovych. (2000) Chaos-hyperchaos transition. Physical Review E 62:2, 1972-1976. Online publication date: 1-Aug-2000. [ CrossRef ]
Malte Schmick, Eric Goles, Mario Markus. (2000) Intermingled basins due to finite accuracy. Physical Review E 62:1, 397-401. Online publication date: 1-Jul-2000. [ CrossRef ]
John Terry, Peter Ashwin. (2000) Comment on “Riddling of Chaotic Sets in Periodic Windows”. Physical Review Letters 85:2, 472-472. Online publication date: 1-Jul-2000. [ CrossRef ]
Ying-Cheng Lai, Celso Grebogi. (2000) Lai and Grebogi Reply:. Physical Review Letters 85:2, 473-473. Online publication date: 1-Jul-2000. [ CrossRef ]
A. V. TABOROV, Yu. L. MAISTRENKO, E. MOSEKILDE. (2000) PARTIAL SYNCHRONIZATION IN A SYSTEM OF COUPLED LOGISTIC MAPS. International Journal of Bifurcation and Chaos 10:05, 1051-1066. Online publication date: 1-May-2000. [ Abstract | PDF (1297 KB) | PDF Plus (465 KB) ]
Matthias Woltering, Mario Markus. (2000) Riddled basins in a model for the Belousov–Zhabotinsky reaction. Chemical Physics Letters 321:5-6, 473-478. Online publication date: 1-May-2000. [ CrossRef ]
David Sweet, Edward Ott. (2000) Fractal dimension of higher-dimensional chaotic repellors. Physica D: Nonlinear Phenomena 139:1-2, 1-27. Online publication date: 1-May-2000. [ CrossRef ]
T. Vadivasova, O. Sosnovtseva, A. Balanov, V. Astakhov. (2000) Desynchronization in coupled systems with quasiperiodic driving. Physical Review E 61:4, 4618-4621. Online publication date: 1-Apr-2000. [ CrossRef ]
P. C Rech, M. W Beims, J. A. C Gallas. (2000) Discovering parameter values by measuring self-similar structures in the phase-space of dissipative systems with constant Jacobian. Europhysics Letters (EPL) 49:6, 702-707. Online publication date: 15-Mar-2000. [ CrossRef ]
Yu Jiang. (2000) Globally coupled maps with time delay interactions. Physics Letters A 267:5-6, 342-349. Online publication date: 1-Mar-2000. [ CrossRef ]
Ranjit Kumar Upadhyay, S.R.K Iyengar, Vikas Rai. (2000) Stability and complexity in ecological systems. Chaos, Solitons & Fractals 11:4, 533-542. Online publication date: 1-Mar-2000. [ CrossRef ]
OSCAR DE FEO, REGIS FERRIERE. (2000) BIFURCATIONS ANALYSIS OF POPULATION INVASION: ON–OFF INTERMITTENCY AND BASIN RIDDLING. International Journal of Bifurcation and Chaos 10:02, 443-452. Online publication date: 1-Feb-2000. [ Abstract | PDF (395 KB) | PDF Plus (282 KB) ]
Akio Hasegawa, Tetsuro Endo, Motomasa Komuro. (2000) On-off intermittency from a ring of four-coupled PLLs. Electronics and Communications in Japan (Part II: Electronics) 83:2, 26-34. Online publication date: 1-Feb-2000. [ CrossRef ]
Ernest Barreto, Paul So, Bruce Gluckman, Steven Schiff. (2000) From Generalized Synchrony to Topological Decoherence: Emergent Sets in Coupled Chaotic Systems. Physical Review Letters 84:8, 1689-1692. Online publication date: 1-Feb-2000. [ CrossRef ]
Yu. MAISTRENKO, O. POPOVYCH, M. HASLER. (2000) ON STRONG AND WEAK CHAOTIC PARTIAL SYNCHRONIZATION. International Journal of Bifurcation and Chaos 10:01, 179-203. Online publication date: 1-Jan-2000. [ Abstract | PDF (1895 KB) | PDF Plus (716 KB) ]
Matthias Woltering, Mario Markus. (2000) Riddled-like Basins of Transient Chaos. Physical Review Letters 84:4, 630-633. Online publication date: 1-Jan-2000. [ CrossRef ]
Vasily Dronov, Edward Ott. (2000) Stalactite basin structure of dynamical systems with transient chaos in an invariant manifold. Chaos: An Interdisciplinary Journal of Nonlinear Science 10:2, 291. Online publication date: 1-Jan-2000. [ CrossRef ]
O. Sosnovtseva, A. Balanov, T. Vadivasova, V. Astakhov, E. Mosekilde. (1999) Loss of lag synchronization in coupled chaotic systems. Physical Review E 60:6, 6560-6565. Online publication date: 1-Dec-1999. [ CrossRef ]
Paul Glendinning. (1999) Transitivity and blowout bifurcations in a class of globally coupled maps. Physics Letters A 264:4, 303-310. Online publication date: 1-Dec-1999. [ CrossRef ]
H. Yang, A. Pikovsky. (1999) Riddling, bubbling, and Hopf bifurcation in coupled map systems. Physical Review E 60:5, 5474-5478. Online publication date: 1-Nov-1999. [ CrossRef ]
Yu.L. Maistrenko, V.L. Maistrenko, O. Popovych, E. Mosekilde. (1999) Unfolding of the riddling bifurcation. Physics Letters A 262:4-5, 355-360. Online publication date: 1-Nov-1999. [ CrossRef ]
Ying-Cheng Lai, Celso Grebogi. (1999) Riddling of Chaotic Sets in Periodic Windows. Physical Review Letters 83:15, 2926-2929. Online publication date: 1-Oct-1999. [ CrossRef ]
Hongyan Sun, Stephen Scott, Kenneth Showalter. (1999) Uncertain destination dynamics. Physical Review E 60:4, 3876-3880. Online publication date: 1-Oct-1999. [ CrossRef ]
Philip J. Aston, Carlo R. Laing. (1999) Symmetry and chaos in the complex Ginzburg-Landau equation - I. Reflectional symmetries. Dynamics and Stability of Systems 14:3, 233-253. Online publication date: 1-Sep-1999. [ CrossRef ]
Yu. Maistrenko, V. Maistrenko, O. Popovych, E. Mosekilde. (1999) Desynchronization of chaos in coupled logistic maps. Physical Review E 60:3, 2817-2830. Online publication date: 1-Sep-1999. [ CrossRef ]
Matthias Woltering, Mario Markus. (1999) Riddled basins of coupled elastic arches. Physics Letters A 260:6, 453-461. Online publication date: 1-Sep-1999. [ CrossRef ]
David Broomhead, Demetris Hadjiloucas, Matthew Nicol. (1999) Random and deterministic perturbation of a class of skew-product systems. Dynamics and Stability of Systems 14:2, 115-128. Online publication date: 1-Jun-1999. [ CrossRef ]
Peter Ashwin, Eurico Covas, Reza Tavakol. (1999) Transverse instability for non-normal parameters. Nonlinearity 12:3, 563-577. Online publication date: 1-May-1999. [ CrossRef ]
Brian Hunt, Edward Ott, Epaminondas Rosa. (1999) Sporadically Fractal Basin Boundaries of Chaotic Systems. Physical Review Letters 82:18, 3597-3600. Online publication date: 1-May-1999. [ CrossRef ]
Ying-Cheng Lai. (1999) Unstable dimension variability and complexity in chaotic systems. Physical Review E 59:4, R3807-R3810. Online publication date: 1-Apr-1999. [ CrossRef ]
Peter Grassberger. (1999) Synchronization of coupled systems with spatiotemporal chaos. Physical Review E 59:3, R2520-R2522. Online publication date: 1-Mar-1999. [ CrossRef ]
T. Kapitaniak, Yu. Maistrenko. (1999) Riddling bifurcations in coupled piecewise linear maps. Physica D: Nonlinear Phenomena 126:1-2, 18-26. Online publication date: 1-Feb-1999. [ CrossRef ]
Laura Gardini, Gian-Italo Bischi, Daniele Fournier-Prunaret. (1999) Basin boundaries and focal points in a map coming from Bairstow’s method. Chaos: An Interdisciplinary Journal of Nonlinear Science 9:2, 367. Online publication date: 1-Jan-1999. [ CrossRef ]
Epaminondas Rosa, Edward Ott. (1999) Mixed basin boundary structures of chaotic systems. Physical Review E 59:1, 343-352. Online publication date: 1-Jan-1999. [ CrossRef ]
Imre Jánosi, Jason Gallas. (1999) Globally coupled multiattractor maps: Mean field dynamics controlled by the number of elements. Physical Review E 59:1, R28-R31. Online publication date: 1-Jan-1999. [ CrossRef ]
Gian-Italo Bischi, Laura Gardini. (1998) Role of invariant and minimal absorbing areas in chaos synchronization. Physical Review E 58:5, 5710-5719. Online publication date: 1-Nov-1998. [ CrossRef ]
Peter Ashwin, A.M. Rucklidge. (1998) Cycling chaos: its creation, persistence and loss of stability in a model of nonlinear magnetoconvection. Physica D: Nonlinear Phenomena 122:1-4, 134-154. Online publication date: 1-Nov-1998. [ CrossRef ]
Christian Beck. (1998) Spontaneous symmetry breaking in a coupled map lattice simulation of quantized Higgs fields. Physics Letters A 248:5-6, 386-392. Online publication date: 1-Nov-1998. [ CrossRef ]
M. Hasler, Yu. Maistrenko, O. Popovych. (1998) Simple example of partial synchronization of chaotic systems. Physical Review E 58:5, 6843-6846. Online publication date: 1-Nov-1998. [ CrossRef ]
Lora Billings, James H. Curry, Eric Phipps. (1998) Symmetric functions and exact Lyapunov exponents. Physica D: Nonlinear Phenomena 121:1-2, 44-64. Online publication date: 1-Oct-1998. [ CrossRef ]
T. Kapitaniak, Yu. Maistrenko. (1998) Multiple choice bifurcations as a source of unpredictability in dynamical systems. Physical Review E 58:4, 5161-5163. Online publication date: 1-Oct-1998. [ CrossRef ]
Ulrike Feudel, Annette Witt, Ying-Cheng Lai, Celso Grebogi. (1998) Basin bifurcation in quasiperiodically forced systems. Physical Review E 58:3, 3060-3066. Online publication date: 1-Sep-1998. [ CrossRef ]
Hava T. Siegelmann, Shmuel Fishman. (1998) Analog computation with dynamical systems. Physica D: Nonlinear Phenomena 120:1-2, 214-235. Online publication date: 1-Sep-1998. [ CrossRef ]
Ling-Yuan Cao, Ying-Cheng Lai. (1998) Antiphase synchronism in chaotic systems. Physical Review E 58:1, 382-386. Online publication date: 1-Jul-1998. [ CrossRef ]
Peter Ashwin, Philip J. Aston. (1998) Blowout bifurcations of codimension two. Physics Letters A 244:4, 261-270. Online publication date: 1-Jul-1998. [ CrossRef ]
Louis Pecora. (1998) Synchronization conditions and desynchronizing patterns in coupled limit-cycle and chaotic systems. Physical Review E 58:1, 347-360. Online publication date: 1-Jul-1998. [ CrossRef ]
T. Kapitaniak, Yu. Maistrenko, A. Stefanski, J. Brindley. (1998) Bifurcations from locally to globally riddled basins. Physical Review E 57:6, R6253-R6256. Online publication date: 1-Jun-1998. [ CrossRef ]
A. Hasegawa, M. Komuro, T. Endo, R. Igarashi. (1998) A new type of intermittency from a ring of four coupled phase-locked loops. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 45:6, 623-633. Online publication date: 1-Jun-1998. [ CrossRef ]
Jeffrey H. Schenker, James W. Swift. (1998) Observing the symmetry of attractors. Physica D: Nonlinear Phenomena 114:3-4, 315-337. Online publication date: 1-Apr-1998. [ CrossRef ]
Alexandre N Carvalho, Hildebrando M Rodrigues, Tomasz Dłotko. (1998) Upper Semicontinuity of Attractors and Synchronization. Journal of Mathematical Analysis and Applications 220:1, 13-41. Online publication date: 1-Apr-1998. [ CrossRef ]
Yu. Maistrenko, V. Maistrenko, A. Popovich, E. Mosekilde. (1998) Transverse instability and riddled basins in a system of two coupled logistic maps. Physical Review E 57:3, 2713-2724. Online publication date: 1-Mar-1998. [ CrossRef ]
V. Paar, N. Pavin. (1998) Intermingled fractal Arnold tongues. Physical Review E 57:2, 1544-1549. Online publication date: 1-Feb-1998. [ CrossRef ]
Yu. Maistrenko, V. Maistrenko, A. Popovich, E. Mosekilde. (1998) Role of the Absorbing Area in Chaotic Synchronization. Physical Review Letters 80:8, 1638-1641. Online publication date: 1-Feb-1998. [ CrossRef ]
M Manscher, M Nordahn, E Mosekilde, Yu.L Maistrenko. (1998) Riddled basins of attraction for synchronized type-I intermittency. Physics Letters A 238:6, 358-364. Online publication date: 1-Feb-1998. [ CrossRef ]
T. Kapitaniak, J. Brindley. (1998) Practical stability of chaotic attractors. Chaos, Solitons & Fractals 9:1-2, 43-50. Online publication date: 1-Jan-1998. [ CrossRef ]
Peter Ashwin, Philip J. Aston, Matthew Nicol. (1998) On the unfolding of a blowout bifurcation. Physica D: Nonlinear Phenomena 111:1-4, 81-95. Online publication date: 1-Jan-1998. [ CrossRef ]
Gian-Italo Bischi, Luciano Stefanini, Laura Gardini. (1998) Synchronization, intermittency and critical curves in a duopoly game. Mathematics and Computers in Simulation 44:6, 559-585. Online publication date: 1-Jan-1998. [ CrossRef ]
T. Kapitaniak, Yu.L. Maistrenko. (1998) Chaos synchronization and riddled basins in two coupled one-dimensional maps. Chaos, Solitons & Fractals 9:1-2, 271-282. Online publication date: 1-Jan-1998. [ CrossRef ]
P Ashwin. (1998) Non-linear dynamics, loss of synchronization and symmetry breaking. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 212:3, 183-187. Online publication date: 1-Jan-1998. [ CrossRef ]
Eurico Covas, Peter Ashwin, Reza Tavakol. (1997) Non-normal parameter blowout bifurcation: An example in a truncated mean-field dynamo model. Physical Review E 56:6, 6451-6458. Online publication date: 1-Dec-1997. [ CrossRef ]
Yu. Maistrenko, T. Kapitaniak, P. Szuminski. (1997) Locally and globally riddled basins in two coupled piecewise-linear maps. Physical Review E 56:6, 6393-6399. Online publication date: 1-Dec-1997. [ CrossRef ]
Ian Melbourne, Ian Stewart. (1997) Symmetric -limit sets for smooth -equivariant dynamical systems with Abelian. Nonlinearity 10:6, 1551-1567. Online publication date: 1-Nov-1997. [ CrossRef ]
Tsuyoshi Chawanya. (1997) Coexistence of infinitely many attractors in a simple flow. Physica D: Nonlinear Phenomena 109:3-4, 201-241. Online publication date: 1-Nov-1997. [ CrossRef ]
M. Hasler, Y.L. Maistrenko. (1997) An introduction to the synchronization of chaotic systems: coupled skew tent maps. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 44:10, 856-866. Online publication date: 1-Oct-1997. [ CrossRef ]
Ying-Cheng Lai. (1997) Scaling laws for noise-induced temporal riddling in chaotic systems. Physical Review E 56:4, 3897-3908. Online publication date: 1-Oct-1997. [ CrossRef ]
A Politi, R Badii. (1997) Dynamical `strangeness' at the edge of chaos. Journal of Physics A: Mathematical and General 30:18, L627-L633. Online publication date: 21-Sep-1997. [ CrossRef ]
Tolga Yalçınkaya, Ying-Cheng Lai. (1997) Bifurcation to strange nonchaotic attractors. Physical Review E 56:2, 1623-1630. Online publication date: 1-Aug-1997. [ CrossRef ]
V. Astakhov, A. Shabunin, T. Kapitaniak, V. Anishchenko. (1997) Loss of Chaos Synchronization through the Sequence of Bifurcations of Saddle Periodic Orbits. Physical Review Letters 79:6, 1014-1017. Online publication date: 1-Aug-1997. [ CrossRef ]
M. Krupa. (1997) Robust heteroclinic cycles. Journal of Nonlinear Science 7:2, 129-176. Online publication date: 1-Apr-1997. [ CrossRef ]
Toni Stojanovski, Ljupco Kocarev, Ulrich Parlitz, Richard Harris. (1997) Sporadic driving of dynamical systems. Physical Review E 55:4, 4035-4048. Online publication date: 1-Apr-1997. [ CrossRef ]
Peter Ashwin. (1997) Cycles homoclinic to chaotic sets; robustness and resonance. Chaos: An Interdisciplinary Journal of Nonlinear Science 7:2, 207. Online publication date: 1-Jan-1997. [ CrossRef ]
Louis M. Pecora, Thomas L. Carroll, Gregg A. Johnson, Douglas J. Mar, James F. Heagy. (1997) Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos: An Interdisciplinary Journal of Nonlinear Science 7:4, 520. Online publication date: 1-Jan-1997. [ CrossRef ]
Hiroyuki Nakajima, Yoshisuke Ueda. (1996) Riddled basins of the optimal states in learning dynamical systems. Physica D: Nonlinear Phenomena 99:1, 35-44. Online publication date: 1-Dec-1996. [ CrossRef ]
Tolga Yalçınkaya, Ying-Cheng Lai. (1996) Blowout Bifurcation Route to Strange Nonchaotic Attractors. Physical Review Letters 77:25, 5039-5042. Online publication date: 1-Dec-1996. [ CrossRef ]
Shankar Venkataramani, Brian Hunt, Edward Ott, Daniel Gauthier, Joshua Bienfang. (1996) Transitions to Bubbling of Chaotic Systems. Physical Review Letters 77:27, 5361-5364. Online publication date: 1-Dec-1996. [ CrossRef ]
Ying-Cheng Lai, Celso Grebogi. (1996) Noise-Induced Riddling in Chaotic Systems. Physical Review Letters 77:25, 5047-5050. Online publication date: 1-Dec-1996. [ CrossRef ]
Ying-Cheng Lai, Celso Grebogi. (1996) Complexity in Hamiltonian-driven dissipative chaotic dynamical systems. Physical Review E 54:5, 4667-4675. Online publication date: 1-Nov-1996. [ CrossRef ]
Yuri Maistrenko, Tomasz Kapitaniak. (1996) Different types of chaos synchronization in two coupled piecewise linear maps. Physical Review E 54:4, 3285-3292. Online publication date: 1-Oct-1996. [ CrossRef ]
Ying-Cheng Lai. (1996) Driving trajectories to a desirable attractor by using small control. Physics Letters A 221:6, 375-383. Online publication date: 1-Oct-1996. [ CrossRef ]
Tomasz Kapitaniak, Karl-Erik Thylwe. (1996) On transverse stability of synchronized chaotic attractors. Chaos, Solitons & Fractals 7:10, 1569-1581. Online publication date: 1-Oct-1996. [ CrossRef ]
Mingzhou Ding, Weiming Yang. (1996) Observation of intermingled basins in coupled oscillators exhibiting synchronized chaos. Physical Review E 54:3, 2489-2494. Online publication date: 1-Sep-1996. [ CrossRef ]
Tomasz Kapitaniak, Karl-Erik Thylwe. (1996) Monotonic stability. Chaos, Solitons & Fractals 7:9, 1411-1415. Online publication date: 1-Sep-1996. [ CrossRef ]
Sebastian Van Strien. (1996) Transitive maps which are not ergodic with respect to Lebesgue measure. Ergodic Theory and Dynamical Systems 16:04, . Online publication date: 1-Aug-1996. [ CrossRef ]
Shankar Venkataramani, Brian Hunt, Edward Ott. (1996) Bubbling transition. Physical Review E 54:2, 1346-1360. Online publication date: 1-Aug-1996. [ CrossRef ]
Yoshihiko Nagai, Xuan-Dong Hua, Ying-Cheng Lai. (1996) Controlling on-off intermittent dynamics. Physical Review E 54:2, 1190-1199. Online publication date: 1-Aug-1996. [ CrossRef ]
James C. Alexander, Brian R. Hunt, Ittai Kan, James A. Yorke. (1996) Intermingled basins for the triangle map. Ergodic Theory and Dynamical Systems 16:04, . Online publication date: 1-Aug-1996. [ CrossRef ]
Brian R. Hunt. (1996) Estimating invariant measures and Lyapunov exponents. Ergodic Theory and Dynamical Systems 16:04, . Online publication date: 1-Aug-1996. [ CrossRef ]
M. Gyllenberg, A. V. Osipov, G. Söderbacka. (1996) Bifurcation analysis of a metapopulation model with sources and sinks. Journal of Nonlinear Science 6:4, 329-366. Online publication date: 1-Jul-1996. [ CrossRef ]
Ying-Cheng Lai. (1996) Distinct small-distance scaling behavior of on-off intermittency in chaotic dynamical systems. Physical Review E 54:1, 321-327. Online publication date: 1-Jul-1996. [ CrossRef ]
Brian Hunt, Edward Ott. (1996) Optimal periodic orbits of chaotic systems occur at low period. Physical Review E 54:1, 328-337. Online publication date: 1-Jul-1996. [ CrossRef ]
Ying-Cheng Lai, Celso Grebogi, James Yorke, S. Venkataramani. (1996) Riddling Bifurcation in Chaotic Dynamical Systems. Physical Review Letters 77:1, 55-58. Online publication date: 1-Jul-1996. [ CrossRef ]
T. Ushio. (1996) Control of chaotic synchronization in composite systems with applications to secure communication systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 43:6, 500-503. Online publication date: 1-Jun-1996. [ CrossRef ]
Tomasz Kapitaniak. (1996) Uncertainty in coupled chaotic systems: Locally intermingled basins of attraction. Physical Review E 53:6, 6555-6557. Online publication date: 1-Jun-1996. [ CrossRef ]
John C. Sommerer, Edward Ott. (1996) Intermingled basins of attraction: uncomputability in a simple physical system. Physics Letters A 214:5-6, 243-251. Online publication date: 1-May-1996. [ CrossRef ]
Peter Ashwin, Jorge Buescu, Ian Stewart. (1996) From attractor to chaotic saddle: a tale of transverse instability. Nonlinearity 9:3, 703-737. Online publication date: 1-May-1996. [ CrossRef ]
Brian Hunt, Edward Ott. (1996) Optimal Periodic Orbits of Chaotic Systems. Physical Review Letters 76:13, 2254-2257. Online publication date: 1-Mar-1996. [ CrossRef ]
Jing-ling Shen, Hua-wei Yin, Jian-hua Dai, Hong-jun Zhang. (1996) Riddled Basin of Laser Cooled-Ions in a Paul Trap. Chinese Physics Letters 13:2, 81-84. Online publication date: 1-Feb-1996. [ CrossRef ]
Ying-Cheng Lai, Celso Grebogi. (1996) Characterizing riddled fractal sets. Physical Review E 53:2, 1371-1374. Online publication date: 1-Feb-1996. [ CrossRef ]
Jennifer Foss, André Longtin, Boualem Mensour, John Milton. (1996) Multistability and Delayed Recurrent Loops. Physical Review Letters 76:4, 708-711. Online publication date: 1-Jan-1996. [ CrossRef ]
Peter Ashwin. (1995) Attractors stuck on to invariant subspaces. Physics Letters A 209:5-6, 338-344. Online publication date: 1-Dec-1995. [ CrossRef ]
J S W Lamb, G R W Quispel. (1995) Cyclic reversing k-symmetry groups. Nonlinearity 8:6, 1005-1026. Online publication date: 1-Nov-1995. [ CrossRef ]
Ying-Cheng Lai, Celso Grebogi. (1995) Intermingled basins and two-state on-off intermittency. Physical Review E 52:4, R3313-R3316. Online publication date: 1-Oct-1995. [ CrossRef ]
Ignacio Pastor-Díaz, Antonio López-Fraguas. (1995) Dynamics of two coupled van der Pol oscillators. Physical Review E 52:2, 1480-1489. Online publication date: 1-Aug-1995. [ CrossRef ]
Ying-Cheng Lai, Raimond Winslow. (1995) Geometric Properties of the Chaotic Saddle Responsible for Supertransients in Spatiotemporal Chaotic Systems. Physical Review Letters 74:26, 5208-5211. Online publication date: 1-Jun-1995. [ CrossRef ]
James Heagy, Louis Pecora, Thomas Carroll. (1995) Short Wavelength Bifurcations and Size Instabilities in Coupled Oscillator Systems. Physical Review Letters 74:21, 4185-4188. Online publication date: 1-May-1995. [ CrossRef ]
T Kapitaniak. (1995) Experimental observation of riddled behaviour (electronic system). Journal of Physics A: Mathematical and General 28:3, L63-L66. Online publication date: 7-Feb-1995. [ CrossRef ]
Ying-Cheng Lai, Grebogi Celso, Eric J. Kostelich. (1994) Extreme final state sensitivity in inhomogeneous spatiotemporal chaotic systems. Physics Letters A 196:3-4, 206-212. Online publication date: 1-Dec-1994. [ CrossRef ]
Ying-Cheng Lai, Celso Grebogi, Eric J. Kostelich. (1994) Extreme final state sensitivity in inhomogeneous spatiotemporal chaotic systems. Physics Letters A 196:1-2, 206-212. Online publication date: 1-Dec-1994. [ CrossRef ]
James Heagy, Thomas Carroll, Louis Pecora. (1994) Experimental and Numerical Evidence for Riddled Basins in Coupled Chaotic Systems. Physical Review Letters 73:26, 3528-3531. Online publication date: 1-Dec-1994. [ CrossRef ]
Ying-Cheng Lai, Raimind Winslow. (1994) Fractal basin boundaries in coupled map lattices. Physical Review E 50:5, 3470-3473. Online publication date: 1-Nov-1994. [ CrossRef ]
Peter Ashwin, Jorge Buescu, Ian Stewart. (1994) Bubbling of attractors and synchronisation of chaotic oscillators. Physics Letters A 193:2, 126-139. Online publication date: 1-Sep-1994. [ CrossRef ]
Edward Ott, J.C. Alexander, I. Kan, J.C. Sommerer, J.A. Yorke. (1994) The transition to chaotic attractors with riddled basins. Physica D: Nonlinear Phenomena 76:4, 384-410. Online publication date: 1-Sep-1994. [ CrossRef ]
J. Heagy, T. Carroll, L. Pecora. (1994) Synchronous chaos in coupled oscillator systems. Physical Review E 50:3, 1874-1885. Online publication date: 1-Sep-1994. [ CrossRef ]
Ying-Cheng Lai, Raimond L. Winslow. (1994) Extreme sensitive dependence on parameters and initial conditions in spatio-temporal chaotic dynamical systems. Physica D: Nonlinear Phenomena 74:3-4, 353-371. Online publication date: 1-Jul-1994. [ CrossRef ]
R.H. Parmenter, L.Y. Yu. (1994) Riddled behavior of certain synchronized systems. Physics Letters A 189:3, 181-186. Online publication date: 1-Jun-1994. [ CrossRef ]
Edward Ott, John C. Sommerer. (1994) Blowout bifurcations: the occurrence of riddled basins and on-off intermittency. Physics Letters A 188:1, 39-47. Online publication date: 1-May-1994. [ CrossRef ]
Ying-Cheng Lai, Raimond Winslow. (1994) Riddled parameter space in spatiotemporal chaotic dynamical systems. Physical Review Letters 72:11, 1640-1643. Online publication date: 1-Mar-1994. [ CrossRef ]
Edward Ott, John Sommerer, James Alexander, Ittai Kan, James Yorke. (1993) Scaling behavior of chaotic systems with riddled basins. Physical Review Letters 71:25, 4134-4137. Online publication date: 1-Dec-1993. [ CrossRef ]