Chaos, Dispersal and Extinction in Coupled Ecosystems

1994

Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent states characterize the long time behavior. An asymptotic analysis is developed by introducing a log-scaled time, and it is shown that such a dynamical process behaves as non-steady weak chaos in which population disturbances grow algebraically in time. Also, some relevance of our study to taxonomic data of biological extinction is mentioned.

Chaotic dynamics are thought to be rare in natural populations, but this may be due to methodological and data limitations, rather than the inherent stability of ecosystems. Following extensive simulation testing, we applied multiple chaos detection methods to a global database of 175 population time series and found evidence for chaos in >30%. In contrast, fitting traditional one-dimensional models identified <10% as chaotic. Chaos was most prevalent among plankton and insects and least among birds and mammals. Lyapunov exponents declined with generation time and scaled as the -1/6 power of mass among chaotic populations. These results demonstrate that chaos is not rare in natural populations, indicating that there may be intrinsic limits to ecological forecasting and cautioning against the use of steady-state approaches to conservation and management.

The European Physical Journal B, 2010

Many theoretical approaches predict the dynamics of interacting populations to be chaotic but that has very rarely been observed in ecological data. It has therefore risen a question about factors that can prevent the onset of chaos by, for instance, making the population fluctuations synchronized over the whole habitat. One such factor is stochasticity. The so-called Moran effect predicts that a spatially correlated noise can synchronize the local population dynamics in a spatially discrete system, thus preventing the onset of spatiotemporal chaos. On the whole, however, the issue of noise has remained controversial and insufficiently understood. In particular, a well-built nonspatial theory infers that noise enhances chaos by making the system more sensitive to the initial conditions. In this paper, we address the problem of the interplay between deterministic dynamics and noise by considering a spatially explicit predatorprey system where some parameters are affected by noise. Our findings are rather counter-intuitive. We show that a small noise (i.e. preserving the deterministic skeleton) can indeed synchronize the population oscillations throughout space and hence keep the dynamics regular, but the dependence of the chaos prevention probability on the noise intensity is of resonance type. Once chaos has developed, it appears to be stable with respect to a small noise but it can be suppressed by a large noise. Finally, we show that our results are in a good qualitative agreement with some available field data.

2001

A traditional assumption in quantitative ecology is that the asymptotic state of the model determines what can be observed in the evolution of the system. It is suggested, however, that irregular transient behaviors may be more relevant than the long term behaviors. Here we investigate how often transient dynamics can be expected in spatially extended ecological systems.

PLoS ONE, 2011

Background: Simple models of insect populations with non-overlapping generations have been instrumental in understanding the mechanisms behind population cycles, including wild (chaotic) fluctuations. The presence of deterministic chaos in natural populations, however, has never been unequivocally accepted. Recently, it has been proposed that the application of chaos control theory can be useful in unravelling the complexity observed in real population data. This approach is based on structural perturbations to simple population models (population skeletons). The mechanism behind such perturbations to control chaotic dynamics thus far is model dependent and constant (in size and direction) through time. In addition, the outcome of such structurally perturbed models is [almost] always equilibrium type, which fails to commensurate with the patterns observed in population data.

Chaos, Solitons & Fractals, 2001

We review our recent eorts to understand why chaotic dynamics is rarely observed in natural populations. The study of two-model ecosystems considered in this paper suggests that chaos exists in narrow parameter ranges. This dynamical behaviour is caused by the crisis-induced sudden death of chaotic attractors. The computed bifurcation diagrams and basin boundary calculations reinforce our earlier conclusion [Chaos, Solitons & Fractals 8 (12) (1997) 1933; Int J Bifurc Chaos 8 (6) (1998) 1325] that the reason why chaos is rarely observed in natural populations is hidden within the mathematical structure of the ecological interactions and not with the problem associated with the data (insucient length, precision, noise, etc.) and its analysis. We also argue that crisis-limited chaotic dynamics can be commonly found in model terrestrial ecosystems. Ó : S 0 9 6 0 -0 7 7 9 ( 0 0 ) 0 0 1 4 1 -7

Physical Review E Statistical Nonlinear and Soft Matter Physics, 2010

The effect of noise on a system of globally coupled chaotic maps is considered. Demographic stochasticity is studied since it provides both noise and a natural definition for extinction. A two-step model is presented, where the intrapatch chaotic dynamics is followed by a migration step with global dispersal. The addition of noise to the already chaotic system is shown to dramatically change its behavior. The level of migration in which the system attains maximal sustainability is identified. This determines the optimal way to manipulate a fragmented habitat in order to conserve endangered species. The quasideterministic dynamics that appears in the large N limit of the stochastic system is analyzed. In the clustering phase, the infinite degeneracy of deterministic solutions emerges from the single steady state of the stochastic system via a mechanism that involves an almost defective Markov matrix.

Iranian Journal of Science and Technology, Transactions A: Science, 2021

The ecological theory of species interactions rests largely on the competition, interference, and predator-prey models. In this paper, we propose and investigate a three-species predator-prey model to inspect the mutual interference between predators. We analyze boundedness and Kolmogorov conditions for the non-spatial model. The dynamical behavior of the system is analyzed by stability and Hopf bifurcation analysis. The Turing instability criteria for the Spatio-temporal system is estimated. In the numerical simulation, phase portrait with time evolution diagrams shows periodic and chaotic oscillations. Bifurcation diagrams show the very rich and complex dynamical behavior of the non-spatial model. We calculate the Lyapunov exponent to justify the dynamics of the non-spatial model. A variety of patterns like interference, spot, and stripe are observed with special emphasis on Beddington-DeAngelis function response. These complex patterns explore the beauty of the spatio-temporal model and it can be easily related to real-world biological systems.

Bulletin of mathematical …, 1999

The possibility of chaos control in biological systems has been stimulated by recent advances in the study of heart and brain tissue dynamics. More recently, some authors have conjectured that such a method might be applied to population dynamics and even play a nontrivial evolutionary role in ecology. In this paper we explore this idea by means of both mathematical and individual-based simulation models. Because of the intrinsic noise linked to individual behavior, controlling a noisy system becomes more difficult but, as shown here, it is a feasible task allowed to be experimentally tested.