Zeta Functions and Continuous Time Dynamics

The major goal of this paper is to explore the effective state estimation algorithm for continuous time dynamic system under the lossy environment without increasing the complexity of hardware realization. Though the existing methods of state estimation of continuous time system provides effective estimation with data loss, the real time hardware realization is difficult due to the complexity and multiple processing. Kalman Filter and Particle Filer are fundamental algorithms for state estimation of any linear and non-linear system respectively, but both have its limitation. The approach adopted here, detect the expected state value and covariance, existed by random input at each stage and filtered the noisy measurement and replace it with predicted modified value for the effective state estimation. To demonstrate the performance of the results, the continuous time dynamics of position of the Aerial Vehicle is used with proposed algorithm under the lossy measurements scenario and compared with standard Kalman filter and smoothed filter. The results show that the proposed method can effectively estimate the position of Aerial Vehicle compared to standard Kalman and smoothed filter under the non-reliable sensor measurements with less hardware realization complexity.

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Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics

Complexity ◽

10.1155/2021/5623783 ◽

2021 ◽

Vol 2021 ◽

pp. 1-24

Author(s):

Héctor A. Echavarria-Heras ◽

Cecilia Leal-Ramírez ◽

Guillermo Gómez ◽

Elia Montiel-Arzate

Keyword(s):

Population Growth ◽

Growth Model ◽

Continuous Time ◽

Extreme Values ◽

Logistic Map ◽

Phase Region ◽

Limiting Factors ◽

Time Dynamics ◽

The Law ◽

Global Trajectory

We examine the comportment of the global trajectory of a piecewisely conceived single species population growth model. Formulation relies on what we develop as the principle of limiting factors for population growth, adapted from the law of the minimum of Liebig and the law of the tolerance of Shelford. The ensuing paradigm sets natality and mortality rates to express through extreme values of population growth determining factor. Dynamics through time occur over different growth phases. Transition points are interpreted as thresholds of viability, starvation, and intraspecific competition. In this delivery, we focus on the qualitative study of the global trajectory expressed on continuous time and on exploring the feasibility of analytical results against data on populations growing under experimental or natural conditions. All study cases sustained fittings of high reproducibility both at empirical and interpretative slants. Possible phase configurations include regimes with multiple stable equilibria, sigmoidal growth, extinction, or stationarity. Here, we also outline that the associating discrete-time piecewise model composes the logistic map applied over a particular region of the phase configuration. Preliminary exploratory analysis suggests that the logistic map’s chaos onset could surpass once the orbit enters a contiguous phase region.

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Biorobots, Nonlinear Dynamics and Perception

Advances in Science and Technology ◽

10.4028/www.scientific.net/ast.58.143 ◽

2008 ◽

Vol 58 ◽

pp. 143-152

Author(s):

Paolo Arena ◽

Davide Lombardo ◽

Luca Patanè

Keyword(s):

Nonlinear Dynamics ◽

Real Time ◽

Continuous Time ◽

Biologically Inspired ◽

Time Dynamics ◽

Nonlinear Network ◽

Biologically Inspired Robots ◽

Novel Approach ◽

Perceptual Control ◽

Efficient Control

In this contribution a survey on a novel approach to locomotion and perception in biologically inspired robots is presented. The basic electronic architecture for modeling and implementing nonlinear dynamics involved in motion and perceptual control of the robot is the Cellular nonlinear network paradigm. It is shown how this continuous time lattice of neural-like circuits can generate suitable and real-time dynamics for efficient control of multi-actuators moving machines, and also to create the basis for a perceptual control of their behaviors.

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CHAOS OF DYNAMICAL SYSTEMS ON GENERAL TIME DOMAINS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409025158 ◽

2009 ◽

Vol 19 (11) ◽

pp. 3829-3832

Author(s):

ABRAHAM BOYARSKY ◽

PAWEŁ GÓRA

Keyword(s):

Dynamical Systems ◽

Discrete Time ◽

Continuous Time ◽

Chaotic Map ◽

Discrete Time System ◽

Combined System ◽

Time Intervals ◽

Time Dynamics ◽

Time Component ◽

Time Domains

We consider dynamical systems on time domains that alternate between continuous time intervals and discrete time intervals. The dynamics on the continuous portions may represent species growth when there is population overlap and are governed by differential or partial differential equations. The dynamics across the discrete time intervals are governed by a chaotic map and may represent population growth which is seasonal. We study the long term dynamics of this combined system. We study various conditions on the continuous time dynamics and discrete time dynamics that produce chaos and alternatively nonchaos for the combined system. When the discrete system alone is chaotic we provide a condition on the continuous dynamical component such that the combined system behaves chaotically. We also provide a condition that ensures that if the discrete time system has an absolutely continuous invariant measure so will the combined system. An example based on the logistic continuous time and logistic discrete time component is worked out.

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