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1.
The qualitative dynamics of a baroclinic flow experiment are studied by constructing phase space coordinates from a single time series. As the stress on the flow is increased we observe steady, periodic, quasiperiodic, and chaotic flow. The chaotic attractor we observe near the transition has the appearance of a thickened torus. 相似文献
2.
A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor. For weak interactions between atoms, periodic motion (antiresonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the condensate manifested by exponential growth in the number of noncondensed atoms. Similar behavior is observed for dynamically localized states (essentially quasiperiodic motions), where stability remains for weak interactions but is destroyed by strong interactions. 相似文献
3.
《Physics letters. A》2020,384(22):126542
We study how the mode of dynamic habitat loss and fragmentation can impact the levels of biodiversity in an ecosystem. The problem is formulated into the framework of resource-based modelling and, opposed to previous studies relying on neutral models, here elements of niche theory are incorporated into the modeling by considering that the species are not ecologically equivalent. In our model the habitat loss is carried out by using a fractal landscape that is constructed through the use of fractional Brownian motion. Thus we can tune the roughness of the landscape by changing the Hurst exponent. We show that both the mode of habitat loss and the level of environmental heterogeneity influence the patterns of species distribution. We notice a larger impact of fragmentation on the number of species when the fragments are more compact. We observe that the relationship between biodiversity and heterogeneity is described by a one-humped function. 相似文献
4.
Hendrik Richter 《Physica D: Nonlinear Phenomena》2008,237(2):167-186
Coupled Map Lattices (CML) can be interpreted as spatio-temporal fitness landscapes which may pose a dynamic optimization problem. In this paper, we analyze such dynamic fitness landscapes in terms of the landscape measures modality, ruggedness, information content and epistasis. These measures account for different aspects of problem hardness. We use an evolutionary algorithm to solve the dynamic optimization problem and study the relationship between performance criteria of the algorithm and the landscape measures. In this way we relate problem hardness to expectable performance. 相似文献
5.
6.
Paulo C. Rech 《中国物理 B》2013,(8):233-237
We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms, and identify various interesting features as a function of two control parameters. In particular, we investigate the emergence of quasiperiodic states arising from Naimark-Sacker bifurcations of stable period-l, period-2, and period-3 orbits. We also investigate the multistability in the same coupling. Lyapunov exponents, parameter planes, phase space portraits, and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states, from quasiperiodic to mode-locked states and to chaotic states, and from chaotic to hyperchaotic states. 相似文献
7.
In this paper we investigate error thresholds on dynamic fitness landscapes. We show that there exists both a lower and an upper threshold, representing limits to the copying fidelity of simple replicators. The lower bound can be expressed as a correction term to the error threshold present on a static landscape. The upper error threshold is a new limit that only exists on dynamic fitness landscapes. We also show that for long genomes and/or highly dynamic fitness landscapes there exists a lower bound on the selection pressure required for the effective selection of genomes with superior fitness independent of mutation rates, i.e. there are distinct nontrivial limits to evolutionary parameters in dynamic environments. 相似文献
8.
Periodic, Quasiperiodic and Chaotic Discrete Breathers in a Parametrical Driven Two-Dimensional Discrete Klein-Gordon Lattice 下载免费PDF全文
We study a two-dimensional lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the two-dimensional Klein-Gordon lattice with hard on-site potential. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers and chaotic discrete breathers by changing the amplitude of the driver. 相似文献
9.
We study a one-dimensional Sine-Gordon lattice of anharmonic oscillators with cubic and quartic nearest-neighbor interactions,
in which discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. DBs can
stably exist in the one-dimensional Sine-Gordon lattice no matter whether the nonlinear interaction is cubic or quartic. When
a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system,
we can obtain the stable quasiperiodic discrete breathers and chaotic discrete breathers by changing the amplitude of the
driver. 相似文献
10.
Bin-bin Lü 《Frontiers of Physics》2010,5(2):199
We study a one-dimensional Sine–Gordon lattice of anharmonic oscillators with cubic and quartic nearest-neighbor interactions, in which discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the one-dimensional Sine–Gordon lattice no matter whether the nonlinear interaction is cubic or quartic. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers and chaotic discrete breathers by changing the amplitude of the driver. 相似文献
11.
We consider a fixed size population that undergoes an evolutionary adaptation in the weak mutation rate limit, which we model
as a biased Langevin process in the genotype space. We show analytically and numerically that, if the fitness landscape has
a small highly epistatic (rough) and time-varying component, then the population genotype exhibits a high effective diffusion
in the genotype space and is able to escape local fitness minima with a large probability. We argue that our principal finding
that even very small time-dependent fluctuations of fitness can substantially speed up evolution is valid for a wide class
of models. 相似文献
12.
The three-dimensional (3-D) dynamics of a fluid-conveying cantilevered pipe fitted with an end-mass and additional intra-span spring-support is investigated in this paper, both theoretically and experimentally. The main objective is to examine how the dynamics of a cantilevered pipe with additional spring-support is modified by the presence of a small mass attached at the free end. In the theoretical study, the nonlinear three-dimensional equations of motion are discretized via Galerkin's method, and the resulting equations are solved by a finite difference method. For the cases studied, the system was found to lose stability by planar flutter; as the flow velocity is increased beyond that point, a sequence of higher order bifurcations ensue, involving 2-D and 3-D periodic and quasiperiodic motions, as well as chaotic ones. In the experiments, performed with elastomer pipes and water flow, similarly 2-D and 3-D periodic, quasiperiodic and chaotic oscillations were observed. Theory and experiments have been shown to be in good qualitative and quantitative agreement. The experimental behaviour is illustrated by video clips (electronic annexes). Moreover, the effects of (i) small stiffness imperfections and (ii) excitation by a point-force are explored theoretically in a preliminary way. 相似文献
13.
We have investigated the appearance of chaos in the one-dimensional Newtonian gravitational three-body system (three masses on a line with -1/r pairwise potential). In the center of mass coordinates this system has two degrees of freedom and can be conveniently studied using Poincare sections. We have concentrated in particular on how the behavior changes when the relative masses of the three bodies change. We consider only the physically more interesting case of negative total energy. For two mass choices we have calculated 18 000 full orbits (with initial states on a 100x180 lattice on the Poincare section) and obtained dwell time distributions. For 105 mass choices we have calculated Poincare maps for 10x18 starting points. Our results show that the Poincare section (and hence the phase space) divides into three well defined regions with orbits of different characteristics: (1) There is a region of fast scattering, with a minimum of pairwise collisions. This region consists of 'scallops' bordering the E=0 line, within a scallop the orbits vary smoothly. The number of the scallops increases as the mass of the central particle decreases. (2) In the chaotic scattering region the interaction times are longer, and both the interaction time and the final state depend sensitively on the starting point on the Poincare section. For both (1) and (2) the initial and final states consist of a binary + single particle. (3) The third region consists of quasiperiodic orbits where the three masses are bound together forever. At the center of the quasiperiodic region there is a periodic orbit discovered (numerically) by Schubart in 1956. The stability of the Schubart orbit turns out to correlate strongly with the global behavior. 相似文献
14.
Evolution is full of coevolving systems characterized by complex spatio-temporal interactions that lead to intertwined processes of adaptation. Yet, how adaptation across multiple levels of temporal scales and biological complexity is achieved remains unclear. Here, we formalize how evolutionary multi-scale processing underlying adaptation constitutes a form of metacognition flowing from definitions of metaprocessing in machine learning. We show (1) how the evolution of metacognitive systems can be expected when fitness landscapes vary on multiple time scales, and (2) how multiple time scales emerge during coevolutionary processes of sufficiently complex interactions. After defining a metaprocessor as a regulator with local memory, we prove that metacognition is more energetically efficient than purely object-level cognition when selection operates at multiple timescales in evolution. Furthermore, we show that existing modeling approaches to coadaptation and coevolution—here active inference networks, predator–prey interactions, coupled genetic algorithms, and generative adversarial networks—lead to multiple emergent timescales underlying forms of metacognition. Lastly, we show how coarse-grained structures emerge naturally in any resource-limited system, providing sufficient evidence for metacognitive systems to be a prevalent and vital component of (co-)evolution. Therefore, multi-scale processing is a necessary requirement for many evolutionary scenarios, leading to de facto metacognitive evolutionary outcomes. 相似文献
15.
Evolution of canalizing Boolean networks 总被引:1,自引:0,他引:1
A. Szejka B. Drossel 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(4):373-380
Boolean networks with canalizing functions are used to model gene regulatory networks. In order to learn how such networks
may behave under evolutionary forces, we simulate the evolution of a single Boolean network by means of an adaptive walk,
which allows us to explore the fitness landscape. Mutations change the connections and the functions of the nodes. Our fitness
criterion is the robustness of the dynamical attractors against small perturbations. We find that with this fitness criterion
the global maximum is always reached and that there is a huge neutral space of 100% fitness. Furthermore, in spite of having
such a high degree of robustness, the evolved networks still share many features with “chaotic” networks. 相似文献
16.
In recent years, it is observed that the third-order explicit autonomous differential equation, named as jerk equation, represents
an interesting sub-class of dynamical systems that can exhibit many major features of the regular and chaotic motion. In this
paper, we investigate the global dynamics of a special family of jerk systems {ie075-01}, whereG(x) is a non-linear function, which are known to exhibit chaotic behaviour at some parameter values. We particularly identify
the regions of parameter space with different asymptotic dynamics using some analytical methods as well as extensive Lyapunov
spectra calculation in complete parameter space. We also investigate the effect of weakening as well as strengthening of the
non-linearity in theG(x) function on the global dynamics of these jerk dynamical systems. As a result, we reach to an important conclusion for these
jerk dynamical systems that a certain amount of non-linearity is sufficient for exhibiting chaotic behaviour but increasing
the non-linearity does not lead to larger regions of parameter space exhibiting chaos. 相似文献
17.
Stochastic time evolution in a nonseparable and nonintegrable quantum system is manifested by rapid dephasing of gaussian wavepackets, whose topological distribution in the coordinate-momentum space defines its irregular regions, while wavepackets initiated in regular regions exhibit quasiperiodic evolution. A gradual transition from quasiperiodic to chaotic dynamics with increasing energy is observed. 相似文献
18.
We present a detailed bifurcation scenario of zero-Prandtl number Rayleigh-Be?nard convection using direct numerical simulations (DNS) and a 27-mode low-dimensional model containing the most energetic modes of DNS. The bifurcation analysis reveals a rich variety of convective flow patterns and chaotic solutions, some of which are common to that of the 13-mode model of Pal et al. [EPL 87, 54003 (2009)]. We also observed a set of periodic and chaotic wavy rolls in DNS and in the model similar to those observed in experiments and numerical simulations. The time period of the wavy rolls is closely related to the eigenvalues of the stability matrix of the Hopf bifurcation points at the onset of convection. This time period is in good agreement with the experimental results for low-Prandtl number fluids. The chaotic attractor of the wavy roll solutions is born through a quasiperiodic and phase-locking route to chaos. 相似文献
19.
In recent years, nonlinear coupled reaction–diffusion (CRD) system has been widely investigated by coupled map lattice method. Previously, nonlinear behaviour was observed dynamically when one or two of the three variables in the discrete system change. In this paper, we consider the chaotic behaviour when three variables change, which is called as four-dimensional chaos. When two parameters in the discrete system are unknown, we first give the existing condition of the chaos in four-dimensional space by the generalized definitions of spatial periodic orbits and spatial chaos. In addition, the chaotic behaviour will vary with the parameters. Then we propose a generalized Lyapunov exponent in four-dimensional space to characterize the different effects of parameters on the chaotic behaviour, which has not been studied in detail. In order to verify the chaotic behaviour of the system and the different effects clearly, we simulate the dynamical behaviour in two- and three-dimensional spaces. 相似文献
20.
Masoller C 《Chaos (Woodbury, N.Y.)》1997,7(3):455-462
This paper presents a spatiotemporal characterization of the dynamics of a single-mode semiconductor laser with optical feedback. I use the two-dimensional representation of a time-delayed system (where the delay time plays the role of a space variable) to represent the time evolution of the output intensity and the phase delay in the external cavity. For low feedback levels the laser output is generally periodic or quasiperiodic and with the 2D representation I obtain quasiperiodic patterns. For higher feedback levels the coherence collapsed regime arises, and in the 2D patterns the quasiperiodic structures break and "defects" appear. In this regime the patterns present features that resemble those of an extended spatiotemporally chaotic system. The 2D representation allows the recognition of two distinct types of transition to coherence collapse. As the feedback intensity grows the number of defects increases and the patterns become increasingly chaotic. As the delay time increases the number of defects in the patterns do not increase and there is a signature of the previous quasiperiodic structure that remains. The nature of the two transitions is understood by examining the behavior of various chaotic indicators (the field autocorrelation function, the Lyapunov spectrum, the fractal dimension, and the metric entropy) when the feedback intensity and the delay time vary. (c) 1997 American Institute of Physics. 相似文献