Multistability: Uncovering hidden attractors

This topical issue collects contributions exemplifying the recent scientific progress in understanding the dynamics of multistable systems. The individual papers focus on different questions of present day interest in theory and applications of systems with multiple attractors. The particular attention is paid to uncovering and characterizing hidden attractors. Both theoretical and experimental studies are presented.

[1]  Tomasz Kapitaniak,et al.  Co-existing attractors of impact oscillator , 1998 .

[2]  T. Kapitaniak,et al.  Stochastic response with bifurcations to non-linear Duffing's oscillator , 1985 .

[3]  U. Feudel,et al.  Control of multistability , 2014 .

[4]  Tomasz Kapitaniak,et al.  Dynamics of impact oscillator with dry friction , 1996 .

[5]  Julien Clinton Sprott,et al.  Simple Chaotic flows with One Stable equilibrium , 2013, Int. J. Bifurc. Chaos.

[6]  T. N. Mokaev,et al.  Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion Homoclinic orbits, and self-excited and hidden attractors , 2015 .

[7]  Nikolay V. Kuznetsov,et al.  Control of multistability in hidden attractors , 2015 .

[8]  Sundarapandian Vaidyanathan,et al.  A 5-D hyperchaotic Rikitake dynamo system with hidden attractors , 2015 .

[9]  Ulrike Feudel,et al.  Multistability, noise, and attractor hopping: the crucial role of chaotic saddles. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  T. E. Vadivasova,et al.  Numerical and experimental studies of attractors in memristor-based Chua’s oscillator with a line of equilibria. Noise-induced effects , 2015 .

[11]  Zhouchao Wei,et al.  Dynamical behaviors of a chaotic system with no equilibria , 2011 .

[12]  Viet-Thanh Pham,et al.  Is that Really Hidden? The Presence of Complex Fixed-Points in Chaotic Flows with No Equilibria , 2014, Int. J. Bifurc. Chaos.

[13]  Przemyslaw Perlikowski,et al.  Multistability and Rare attractors in van der Pol-Duffing oscillator , 2011, Int. J. Bifurc. Chaos.

[14]  Yu Feng,et al.  Switched generalized function projective synchronization of two hyperchaotic systems with hidden attractors , 2015 .

[15]  Tomasz Kapitaniak,et al.  Multi-headed chimera states in coupled pendula , 2015 .

[16]  T. Kapitaniak,et al.  NOISE-ENHANCED PHASE LOCKING IN A STOCHASTIC BISTABLE SYSTEM DRIVEN BY A CHAOTIC SIGNAL , 1999 .

[17]  Nikolay V. Kuznetsov,et al.  Analytical-numerical method for attractor localization of generalized Chua's system , 2010, PSYCO.

[18]  G. Leonov,et al.  Localization of hidden Chuaʼs attractors , 2011 .

[19]  Sundarapandian Vaidyanathan,et al.  Hidden attractors in a chaotic system with an exponential nonlinear term , 2015 .

[20]  Przemyslaw Perlikowski,et al.  Synchronization and multistability in the ring of modified Rössler oscillators , 2015 .

[21]  Nikolay V. Kuznetsov,et al.  Hidden attractor in smooth Chua systems , 2012 .

[22]  Kapitaniak.  Generating strange nonchaotic trajectories. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  Julien Clinton Sprott,et al.  Strange attractors with various equilibrium types , 2015 .

[24]  Nikolay V. Kuznetsov,et al.  Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems , 2011 .

[25]  Tomasz Kapitaniak,et al.  Rare and hidden attractors in Van der Pol-Duffing oscillators , 2015 .

[26]  Viet-Thanh Pham,et al.  Constructing a Novel No-Equilibrium Chaotic System , 2014, Int. J. Bifurc. Chaos.

[27]  Alexander N. Pisarchik,et al.  Controlling bistability in a stochastic perception model , 2015 .

[28]  Julien Clinton Sprott,et al.  Multistability in symmetric chaotic systems , 2015 .

[29]  Nikolay V. Kuznetsov,et al.  Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua’s circuits , 2011 .

[30]  Zhouchao Wei,et al.  Delayed feedback control and bifurcation analysis of the generalized Sprott B system with hidden attractors , 2015 .

[31]  Julien Clinton Sprott,et al.  A dynamical system with a strange attractor and invariant tori , 2014 .

[32]  Tomasz Kapitaniak,et al.  Noise-induced basin hopping in a vibro-impact system , 2007 .

[33]  James A. Yorke,et al.  Dynamics: Numerical Explorations , 1994 .

[34]  Viet-Thanh Pham,et al.  Synchronization and circuit design of a chaotic system with coexisting hidden attractors , 2015 .

[35]  Julien Clinton Sprott,et al.  Simple chaotic flows with a line equilibrium , 2013 .

[36]  Sergey P. Kuznetsov,et al.  Co-existing hidden attractors in a radio-physical oscillator system , 2015 .

[37]  Alexander Medvedev,et al.  Multistability and hidden attractors in an impulsive Goodwin oscillator with time delay , 2015 .

[38]  Julien Clinton Sprott,et al.  Recent new examples of hidden attractors , 2015 .

[39]  Ulrike Feudel,et al.  Complex Dynamics in multistable Systems , 2008, Int. J. Bifurc. Chaos.

[40]  Ramakrishna Ramaswamy,et al.  The Nature of Attractor Basins in multistable Systems , 2008, Int. J. Bifurc. Chaos.

[41]  Anirban Ray,et al.  Memristive non-linear system and hidden attractor , 2015, The European Physical Journal Special Topics.

[42]  Awadhesh Prasad,et al.  Complicated basins and the phenomenon of amplitude death in coupled hidden attractors , 2014 .