Destabilization and chaos induced by harvesting: insights from one-dimensional discrete-time models

2021 ◽  
Vol 82 (1-2) ◽  
Author(s):  
Víctor Jiménez López ◽  
Eduardo Liz
Keyword(s):  
Discrete Time ◽  
One Dimensional ◽  
Discrete Time Models

MODELING AND BIFURCATION BEHAVIOR OF MULTI-PHASE SIMIMO DC–DC SWITCHING REGULATORS

2010 ◽  
Vol 20 (11) ◽  
pp. 3841-3861 ◽  
Author(s):  
V. MORENO-FONT ◽  
A. EL AROUDI ◽  
L. BENADERO
Keyword(s):  
Discrete Time ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Dynamical Behavior ◽  
Stability Index ◽  
Operating Conditions ◽  
Continuation Methods ◽  
Accurate Information ◽  
One Dimensional ◽  
Discrete Time Models

In this paper, different discrete-time models in the form of maps are proposed and analyzed in order to describe the dynamics of single inductor multiple-input multiple-output (SIMIMO) switching DC–DC converters. These systems can be used to regulate generally multiple (positive and/or negative) outputs by means of individual switches associated to each of the outputs. These switches are current mode controlled through corresponding channels. The discrete-time approach allows the dynamical behavior of these systems to be accurately predicted as well as to detect possible subharmonic oscillations and chaotic behavior. Under certain operating conditions, for which the system can be modeled by a one-dimensional piecewise constant vector field, a simple one-dimensional and piecewise-linear (PWL) map can be obtained. Some closed form expressions for ensuring stability are derived from this map in terms of a stability index λ, which is, in turn, expressed in terms of system parameters. However, some discrepancies have been found between the switched model and this simpler map, and therefore a full order model is derived to obtain more accurate information about the actual dynamical behavior of these converters. The theoretical results are confirmed by one-dimensional bifurcation diagrams and codimension 1 two-parameter bifurcation curves obtained by standard continuation methods applied to the derived discrete-time models as well as from computer simulations from the switched model.

scholarly journals Semiglobal exponential input-to-state stability of sampled-data systems based on approximate discrete-time models

Automatica ◽  
2021 ◽  
Vol 131 ◽  
pp. 109742
Author(s):  
Alexis J. Vallarella ◽  
Paula Cardone ◽  
Hernan Haimovich
Keyword(s):  
Discrete Time ◽  
Data Systems ◽  
Sampled Data ◽  
Discrete Time Models

Discrete-Time Memristor Model for Enhancing Chaotic Complexity and Application in Secure Communication

2022 ◽  
Author(s):  
Wenhao Yan ◽  
Zijing Jiang ◽  
Qun Ding
Keyword(s):  
Fixed Points ◽  
Discrete Time ◽  
Dynamic Characteristics ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Two Dimensional ◽  
Initial State ◽  
One Dimensional ◽  
Backward Euler ◽  
Short Period

Abstract The physical implementation of continuoustime memristor makes it widely used in chaotic circuits, whereas discrete-time memristor has not received much attention. In this paper, the backward-Euler method is used to discretize TiO2 memristor model, and the discretized model also meets the three fingerprinter characteristics of the generalized memristor. The short period phenomenon and uneven output distribution of one-dimensional chaotic systems affect their applications in some fields, so it is necessary to improve the dynamic characteristics of one-dimensional chaotic systems. In this paper, a two-dimensional discrete-time memristor model is obtained by linear coupling the proposed TiO2 memristor model and one-dimensional chaotic systems. Since the two-dimensional model has infinite fixed points, the stability of these fixed points depends on the coupling parameters and the initial state of the discrete TiO2 memristor model. Furthermore, the dynamic characteristics of one-dimensional chaotic systems can be enhanced by the proposed method. Finally, we apply the generated chaotic sequence to secure communication.

scholarly journals Discrete-time quantum walks generated by aperiodic fractal sequence of space coin operators

2018 ◽  
Vol 29 (10) ◽  
pp. 1850098 ◽  
Author(s):  
R. F. S. Andrade ◽  
A. M. C. Souza
Keyword(s):  
Wave Function ◽  
Probability Distribution ◽  
Discrete Time ◽  
Numerical Study ◽  
Entanglement Entropy ◽  
Quantum Effects ◽  
Quantum Walks ◽  
Cantor Set ◽  
One Dimensional ◽  
Time Quantum

Properties of one-dimensional discrete-time quantum walks (DTQWs) are sensitive to the presence of inhomogeneities in the substrate, which can be generated by defining position-dependent coin operators. Deterministic aperiodic sequences of two or more symbols provide ideal environments where these properties can be explored in a controlled way. Based on an exhaustive numerical study, this work discusses a two-coin model resulting from the construction rules that lead to the usual fractal Cantor set. Although the fraction of the less frequent coin [Formula: see text] as the size of the chain is increased, it leaves peculiar properties in the walker dynamics. They are characterized by the wave function, from which results for the probability distribution and its variance, as well as the entanglement entropy, were obtained. A number of results for different choices of the two coins are presented. The entanglement entropy has shown to be very sensitive to uncovering subtle quantum effects present in the model.

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