Chaotic Dynamical System in Ecology Research Papers (original) (raw)

In this paper we develop a general approach for investigating the asymptotic distribution of functionals Xn = f((Zn+k)k2Z) of absolutely reg- ular stochastic processes (Zn)n2Z. Such functionals occur naturally as orbits of chaotic... more

In this paper we develop a general approach for investigating the asymptotic distribution of functionals Xn = f((Zn+k)k2Z) of absolutely reg- ular stochastic processes (Zn)n2Z. Such functionals occur naturally as orbits of chaotic dynamical systems, and thus our results can be used to study proba- bilistic aspects of dynamical systems. We rst prove some moment inequalities that are analogous to

This paper presents the new Lorenz unlike chaotic attractor which is constructed by a three non linear first order differential equations. These equations are arranged in a three dimensional autonomous systems. The dynamic behavior of the... more

This paper presents the new Lorenz unlike chaotic attractor which is constructed by a three non linear first order differential equations. These equations are arranged in a three dimensional autonomous systems. The dynamic behavior of the new chaotic system is shown such as time series, strange attractors, and bifurcations. Numerical experience also shows that when the parameter 'd' is varied, the global non linear amplitude is also varying. The paper ends with some possible research and development recommendations.

We study two dynamical properties of linear D-dimensional cellular automata over Zm namely, denseness of periodic points and topological mixing. For what concerns denseness of periodic points, we complete the work initiated in (Theoret.... more

We study two dynamical properties of linear D-dimensional cellular automata over Zm namely, denseness of periodic points and topological mixing. For what concerns denseness of periodic points, we complete the work initiated in (Theoret. Comput. Sci. 174 (1997) 157, Theoret. Comput. Sci. 233 (1–2) (2000) 147, 14th Annual Symp. on Theoretical Aspects of Computer Science (STACS ’97), LNCS n. 1200,

In this paper, a method of estimating the dimension of dynamical systems from a time series, using neural networks, is examined. It is based (a) on the hypothesis that a member of a time series can be optimally expressed as a... more

In this paper, a method of estimating the dimension of dynamical systems from a time series, using neural networks, is examined. It is based (a) on the hypothesis that a member of a time series can be optimally expressed as a deterministic function of the d past series values (where d is the dimension of the system), and (b) on the observation that neural networks’learning ability is improved rapidly when the appropriate amount of information is provided to a neural structure which is as complex as needed. To estimate the dimension of a dynamical system, neural networks are trained to learn the component of the attractor expressed by a reconstructed vector in a suitable phase space whose embedding dimension m, has been estimated using the mutual information method. More specifically, the information supplied to the networks is represented by vectors consisting of the m past values of the time series, where m varies from 1 to D + 2, D being a pre-estimation for the maximum value of t...

We develop novel methods to compute auto-correlation functions, or power spectral densi-ties, for chaotic dynamical systems generated by an inverse method whose starting point is an invariant distribution and a two-form. In general, the... more

We develop novel methods to compute auto-correlation functions, or power spectral densi-ties, for chaotic dynamical systems generated by an inverse method whose starting point is an invariant distribution and a two-form. In general, the inverse method makes some aspects ...

Periodic orbit analysis at the onset of the unstable dimension variability and at the blowout bifurcation. [Chaos: An Interdisciplinary Journal of Nonlinear Science 17, 023131 (2007)]. RF Pereira, SE de S. Pinto, RL Viana, SR Lopes, C.... more

Periodic orbit analysis at the onset of the unstable dimension variability and at the blowout bifurcation. [Chaos: An Interdisciplinary Journal of Nonlinear Science 17, 023131 (2007)]. RF Pereira, SE de S. Pinto, RL Viana, SR Lopes, C. Grebogi. Abstract. ...

We propose a plain files cipher by means of a stream cryptosystem scheme with chaotic addition and a symmetric key. The sequence of numbers used for encryption is generated by a continuous chaotic dynamical system; in particular, we... more

We propose a plain files cipher by means of a stream cryptosystem scheme with chaotic addition and a symmetric key. The sequence of numbers used for encryption is generated by a continuous chaotic dynamical system; in particular, we choose the forced Duffing equation since this kind of systems is sensitive to the initial conditions. In a chaotic system, the answer

The major goal of the present paper is to find out the manifestation of the boundedness of fluctuations. Two different subjects are considered: (i) an ergodic Markovian process associated with a new type of large scale fluctuations at... more

The major goal of the present paper is to find out the manifestation of the boundedness of fluctuations. Two different subjects are considered: (i) an ergodic Markovian process associated with a new type of large scale fluctuations at spatially homogeneous reaction systems; (ii) simulated dynamical systems that possess strange attractors. Their common property is that the fluctuations are bounded. It is found out that the mathematical description of the stochasticity at both types of systems is identical. Then, it is to be expected that it exhibits certain common features whose onset is the stochasticity, namely: (i) The power spectrum of a time series of length T comprises a striclty decreasing band that uniformly fits the shape 1/fα(f) where [Formula: see text] and α(f) strictly increases to the value α(∞) = p(p…

In the present work, Lyapunov stability theory, non linear adaptive control law and the parameter updat e law were utilized to derive the state of two new ch aotic reversal systems after being synchronized by the function projective... more

In the present work, Lyapunov stability theory, non
linear adaptive control law and the parameter updat
e
law were utilized to derive the state of two new ch
aotic reversal systems after being synchronized by
the
function projective method. Using this technique al
lows for a scaling function instead of a constant t
hereby
giving a better method in applications in secure co
mmunication. Numerical simulations are presented to
demonstrate the effective nature of the proposed sc
heme of synchronization for the new chaotic reversa
l
system.

We present a new method to combine possibly inconsistent locally (piecewise) trained conditional models p (y α| x α) into pseudo-samples from a global model. Our method does not require training of a CRF, but instead generates samples by... more

We present a new method to combine possibly inconsistent locally (piecewise) trained conditional models p (y α| x α) into pseudo-samples from a global model. Our method does not require training of a CRF, but instead generates samples by iterating forward a weakly chaotic dynamical system. The new method is illustrated on image segmentation tasks where classifiers based on local appearance cues are combined with pairwise boundary cues.