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Kedia H, Pan D, Slotine JJ, England JL. Drive-specific selection in multistable mechanical networks. J Chem Phys 2023; 159:214106. [PMID: 38047510 DOI: 10.1063/5.0171993] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 11/05/2023] [Indexed: 12/05/2023] Open
Abstract
Systems with many stable configurations abound in nature, both in living and inanimate matter, encoding a rich variety of behaviors. In equilibrium, a multistable system is more likely to be found in configurations with lower energy, but the presence of an external drive can alter the relative stability of different configurations in unexpected ways. Living systems are examples par excellence of metastable nonequilibrium attractors whose structure and stability are highly dependent on the specific form and pattern of the energy flow sustaining them. Taking this distinctively lifelike behavior as inspiration, we sought to investigate the more general physical phenomenon of drive-specific selection in nonequilibrium dynamics. To do so, we numerically studied driven disordered mechanical networks of bistable springs possessing a vast number of stable configurations arising from the two stable rest lengths of each spring, thereby capturing the essential physical properties of a broad class of multistable systems. We found that there exists a range of forcing amplitudes for which the attractor states of driven disordered multistable mechanical networks are fine-tuned with respect to the pattern of external forcing to have low energy absorption from it. Additionally, we found that these drive-specific attractor states are further stabilized by precise matching between the multidimensional shape of their orbit and that of the potential energy well they inhabit. Lastly, we showed evidence of drive-specific selection in an experimental system and proposed a general method to estimate the range of drive amplitudes for drive-specific selection.
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Affiliation(s)
- Hridesh Kedia
- Physics of Living Systems Group, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Deng Pan
- Physics of Living Systems Group, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jean-Jacques Slotine
- Nonlinear Systems Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Schoenmakers S, Feudel U. A resilience concept based on system functioning: A dynamical systems perspective. CHAOS (WOODBURY, N.Y.) 2021; 31:053126. [PMID: 34240958 DOI: 10.1063/5.0042755] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2021] [Accepted: 04/21/2021] [Indexed: 06/13/2023]
Abstract
We introduce a new framework for resilience, which is traditionally understood as the ability of a system to absorb disturbances and maintain its state, by proposing a shift from a state-based to a system functioning-based approach to resilience, which takes into account that several different coexisting stable states could fulfill the same functioning. As a consequence, not every regime shift, i.e., transition from one stable state to another, is associated with a lack or loss of resilience. We emphasize the importance of flexibility-the ability of a system to shift between different stable states while still maintaining system functioning. Furthermore, we provide a classification of system responses based on the phenomenological properties of possible disturbances, including the role of their timescales. Therefore, we discern fluctuations, shocks, press disturbances, and trends as possible disturbances. We distinguish between two types of mechanisms of resilience: (i) tolerance and flexibility, which are properties of the system, and (ii) adaptation and transformation, which are processes that alter the system's tolerance and flexibility. Furthermore, we discuss quantitative methods to investigate resilience in model systems based on approaches developed in dynamical systems theory.
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Affiliation(s)
- Sarah Schoenmakers
- Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University of Oldenburg, 26111 Oldenburg, Germany
| | - Ulrike Feudel
- Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University of Oldenburg, 26111 Oldenburg, Germany
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Coexistence of hidden attractors, 2-torus and 3-torus in a new simple 4-D chaotic system with hyperbolic cosine nonlinearity. ACTA ACUST UNITED AC 2018. [DOI: 10.1007/s40435-017-0392-9] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Szabo E. Oregonator generalization as a minimal model of quorum sensing in Belousov–Zhabotinsky reaction with catalyst confinement in large populations of particles. RSC Adv 2015. [DOI: 10.1039/c5ra12841b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
The Oregonator demonstrates that quorum sensing in populations of Belousov–Zhabotinsky oscillators arises from modification of the stoichiometry by catalyst confinement.
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Affiliation(s)
- E. Szabo
- Department of Earth and Planetary Sciences
- Harvard University
- Cambridge
- USA
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Patel MS, Patel U, Sen A, Sethia GC, Hens C, Dana SK, Feudel U, Showalter K, Ngonghala CN, Amritkar RE. Experimental observation of extreme multistability in an electronic system of two coupled Rössler oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022918. [PMID: 25353556 DOI: 10.1103/physreve.89.022918] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2013] [Indexed: 06/04/2023]
Abstract
We report the first experimental observation of extreme multistability in a controlled laboratory investigation. Extreme multistability arises when infinitely many attractors coexist for the same set of system parameters. The behavior was predicted earlier on theoretical grounds, supported by numerical studies of models of two coupled identical or nearly identical systems. We construct and couple two analog circuits based on a modified coupled Rössler system and demonstrate the occurrence of extreme multistability through a controlled switching to different attractor states purely through a change in initial conditions for a fixed set of system parameters. Numerical studies of the coupled model equations are in agreement with our experimental findings.
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Affiliation(s)
- Mitesh S Patel
- Institute for Plasma Research, Bhat, Gandhinagar 382 428, India
| | - Unnati Patel
- Institute for Plasma Research, Bhat, Gandhinagar 382 428, India
| | - Abhijit Sen
- Institute for Plasma Research, Bhat, Gandhinagar 382 428, India
| | - Gautam C Sethia
- Institute for Plasma Research, Bhat, Gandhinagar 382 428, India
| | | | - Syamal K Dana
- CSIR-Indian Institute of Chemical Biology, Kolkata, India
| | - Ulrike Feudel
- Institute for Chemistry and Biology of the Marine Environment, University of Oldenburg, Oldenberg, Germany and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742-2431, USA
| | - Kenneth Showalter
- C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045, USA
| | - Calistus N Ngonghala
- National Institute for Mathematical and Biological Synthesis, University of Tennessee, Knoxville, Tennessee 37996, USA
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Ngonghala CN, Feudel U, Showalter K. Extreme multistability in a chemical model system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:056206. [PMID: 21728629 DOI: 10.1103/physreve.83.056206] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2010] [Indexed: 05/31/2023]
Abstract
Coupled systems can exhibit an unusual kind of multistability, namely, the coexistence of infinitely many attractors for a given set of parameters. This extreme multistability is demonstrated to occur in coupled chemical model systems with various types of coupling. We show that the appearance of extreme multistability is associated with the emergence of a conserved quantity in the long-term limit. This conserved quantity leads to a "slicing" of the state space into manifolds corresponding to the value of the conserved quantity. The state space "slices" develop as t→∞ and there exists at least one attractor in each of them. We discuss the dependence of extreme multistability on the coupling and on the mismatch of parameters of the coupled systems.
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Affiliation(s)
- Calistus N Ngonghala
- Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506-6310, USA
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Feudel U, Grebogi C. Why are chaotic attractors rare in multistable systems? PHYSICAL REVIEW LETTERS 2003; 91:134102. [PMID: 14525307 DOI: 10.1103/physrevlett.91.134102] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/1999] [Revised: 10/30/2002] [Indexed: 05/24/2023]
Abstract
We show that chaotic attractors are rarely found in multistable dissipative systems close to the conservative limit. As we approach this limit, the parameter intervals for the existence of chaotic attractors as well as the volume of their basins of attraction in a bounded region of the state space shrink very rapidly. An important role in the disappearance of these attractors is played by particular points in parameter space, namely, the double crises accompanied by a basin boundary metamorphosis. Scaling relations between successive double crises are presented. Furthermore, along this path of double crises, we obtain scaling laws for the disappearance of chaotic attractors and their basins of attraction.
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Kraut S, Feudel U. Multistability, noise, and attractor hopping: the crucial role of chaotic saddles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:015207. [PMID: 12241417 DOI: 10.1103/physreve.66.015207] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2001] [Revised: 05/03/2002] [Indexed: 05/23/2023]
Abstract
We investigate the hopping dynamics between different attractors in a multistable system under the influence of noise. Using symbolic dynamics we find a sudden increase of dynamical entropies, when a system parameter is varied. This effect is explained by a bifurcation involving two chaotic saddles. We also demonstrate that the transient lifetimes on the saddle obey a scaling law in analogy to crisis.
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Affiliation(s)
- Suso Kraut
- Institut für Physik, Universität Potsdam, Postfach 601553, D-14415 Potsdam, Germany
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Barragán D, Eu BC. Propagation Failure in an Array of Oregonator Cells and Irreversible Thermodynamics of an Assembly of Discrete Systems. J Phys Chem A 2002. [DOI: 10.1021/jp012854r] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Daniel Barragán
- Departamento de Química, Facultad de Cienceias, Universidad Nacional de Colombia, Bogota, Columbia
| | - Byung Chan Eu
- Department of Chemistry and Centre for the Physics of Materials, McGill University, 801 Sherbrooke St. West, Montreal, Quebec H3A 2K6, Canada
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Gadaleta S, Dangelmayr G. Learning to control a complex multistable system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:036217. [PMID: 11308751 DOI: 10.1103/physreve.63.036217] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2000] [Revised: 09/19/2000] [Indexed: 05/23/2023]
Abstract
In this paper the control of a periodically kicked mechanical rotor without gravity in the presence of noise is investigated. In recent work it was demonstrated that this system possesses many competing attracting states and thus shows the characteristics of a complex multistable system. We demonstrate that it is possible to stabilize the system at a desired attracting state even in the presence of high noise level. The control method is based on a recently developed algorithm [S. Gadaleta and G. Dangelmayr, Chaos 9, 775 (1999)] for the control of chaotic systems and applies reinforcement learning to find a global optimal control policy directing the system from any initial state towards the desired state in a minimum number of iterations. Being data-based, the method does not require any information about governing dynamical equations.
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Affiliation(s)
- S Gadaleta
- Department of Mathematics, Colorado State University, Weber Building, Fort Collins, Colorado 80523, USA.
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Kraut S, Feudel U, Grebogi C. Preference of attractors in noisy multistable systems. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 59:5253-60. [PMID: 11969483 DOI: 10.1103/physreve.59.5253] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/1998] [Indexed: 04/18/2023]
Abstract
A model system exhibiting a large number of attractors is investigated under the influence of noise. Several methods for discriminating two qualitatively different regions of the noise intensity are presented, and the phenomenon of noise-induced preference of attractors is reported. Finally, the relevance of our findings for detection of multiple stable states of systems occurring in nature or in the laboratory is pointed out.
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Affiliation(s)
- S Kraut
- Institut für Physik, Universität Potsdam, Postfach 601553, D-14415 Potsdam, Germany
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Feudel U, Grebogi C. Multistability and the control of complexity. CHAOS (WOODBURY, N.Y.) 1997; 7:597-604. [PMID: 12779685 DOI: 10.1063/1.166259] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We show how multistability arises in nonlinear dynamics and discuss the properties of such a behavior. In particular, we show that most attractors are periodic in multistable systems, meaning that chaotic attractors are rare in such systems. After arguing that multistable systems have the general traits expected from a complex system, we pass to control them. Our controlling complexity ideas allow for both the stabilization and destabilization of any one of the coexisting states. The control of complexity differs from the standard control of chaos approach, an approach that makes use of the unstable periodic orbits embedded in an extended chaotic attractor. (c) 1997 American Institute of Physics.
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Affiliation(s)
- Ulrike Feudel
- Institut fur Physik, Universitat Potsdam, PF 601553, D-14415 Potsdam, Germany
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