2,876 research outputs found
Boolean Delay Equations: A simple way of looking at complex systems
Boolean Delay Equations (BDEs) are semi-discrete dynamical models with
Boolean-valued variables that evolve in continuous time. Systems of BDEs can be
classified into conservative or dissipative, in a manner that parallels the
classification of ordinary or partial differential equations. Solutions to
certain conservative BDEs exhibit growth of complexity in time. They represent
therewith metaphors for biological evolution or human history. Dissipative BDEs
are structurally stable and exhibit multiple equilibria and limit cycles, as
well as more complex, fractal solution sets, such as Devil's staircases and
``fractal sunbursts``. All known solutions of dissipative BDEs have stationary
variance. BDE systems of this type, both free and forced, have been used as
highly idealized models of climate change on interannual, interdecadal and
paleoclimatic time scales. BDEs are also being used as flexible, highly
efficient models of colliding cascades in earthquake modeling and prediction,
as well as in genetics. In this paper we review the theory of systems of BDEs
and illustrate their applications to climatic and solid earth problems. The
former have used small systems of BDEs, while the latter have used large
networks of BDEs. We moreover introduce BDEs with an infinite number of
variables distributed in space (``partial BDEs``) and discuss connections with
other types of dynamical systems, including cellular automata and Boolean
networks. This research-and-review paper concludes with a set of open
questions.Comment: Latex, 67 pages with 15 eps figures. Revised version, in particular
the discussion on partial BDEs is updated and enlarge
Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey
The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H ∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out
Mathematical control of complex systems 2013
Mathematical control of complex systems have already become an ideal research area for control engineers, mathematicians, computer scientists, and biologists to understand, manage, analyze, and interpret functional information/dynamical behaviours from real-world complex dynamical systems, such as communication systems, process control, environmental systems, intelligent manufacturing systems, transportation systems, and structural systems. This special issue aims to bring together the latest/innovative knowledge and advances in mathematics for handling complex systems. Topics include, but are not limited to the following: control systems theory (behavioural systems, networked control systems, delay systems, distributed systems, infinite-dimensional systems, and positive systems); networked control (channel capacity constraints, control over communication networks, distributed filtering and control, information theory and control, and sensor networks); and stochastic systems (nonlinear filtering, nonparametric methods, particle filtering, partial identification, stochastic control, stochastic realization, system identification)
Vectorial dissipative solitons in vertical-cavity surface-emitting Lasers with delays
We show that the nonlinear polarization dynamics of a vertical-cavity
surface-emitting laser placed into an external cavity leads to the formation of
temporal vectorial dissipative solitons. These solitons arise as cycles in the
polarization orientation, leaving the total intensity constant. When the cavity
round-trip is much longer than their duration, several independent solitons as
well as bound states (molecules) may be hosted in the cavity. All these
solutions coexist together and with the background solution, i.e. the solution
with zero soliton. The theoretical proof of localization is given by the
analysis of the Floquet exponents. Finally, we reduce the dynamics to a single
delayed equation for the polarization orientation allowing interpreting the
vectorial solitons as polarization kinks.Comment: quasi final resubmission version, 12 pages, 9 figure
Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics
Neural activity patterns related to behavior occur at many scales in time and
space from the atomic and molecular to the whole brain. Here we explore the
feasibility of interpreting neurophysiological data in the context of many-body
physics by using tools that physicists have devised to analyze comparable
hierarchies in other fields of science. We focus on a mesoscopic level that
offers a multi-step pathway between the microscopic functions of neurons and
the macroscopic functions of brain systems revealed by hemodynamic imaging. We
use electroencephalographic (EEG) records collected from high-density electrode
arrays fixed on the epidural surfaces of primary sensory and limbic areas in
rabbits and cats trained to discriminate conditioned stimuli (CS) in the
various modalities. High temporal resolution of EEG signals with the Hilbert
transform gives evidence for diverse intermittent spatial patterns of amplitude
(AM) and phase modulations (PM) of carrier waves that repeatedly re-synchronize
in the beta and gamma ranges at near zero time lags over long distances. The
dominant mechanism for neural interactions by axodendritic synaptic
transmission should impose distance-dependent delays on the EEG oscillations
owing to finite propagation velocities. It does not. EEGs instead show evidence
for anomalous dispersion: the existence in neural populations of a low velocity
range of information and energy transfers, and a high velocity range of the
spread of phase transitions. This distinction labels the phenomenon but does
not explain it. In this report we explore the analysis of these phenomena using
concepts of energy dissipation, the maintenance by cortex of multiple ground
states corresponding to AM patterns, and the exclusive selection by spontaneous
breakdown of symmetry (SBS) of single states in sequences.Comment: 31 page
Laminar chaos in systems with quasiperiodic delay
A new type of chaos called laminar chaos was found in singularly perturbed
dynamical systems with periodic time-varying delay [Phys. Rev. Lett. 120,
084102 (2018)]. It is characterized by nearly constant laminar phases, which
are periodically interrupted by irregular bursts, where the intensity levels of
the laminar phases vary chaotically from phase to phase. In this paper, we
demonstrate that laminar chaos can also be observed in systems with
quasiperiodic delay, where we generalize the concept of conservative and
dissipative delays to such systems. It turns out that the durations of the
laminar phases vary quasiperiodically and follow the dynamics of a torus map in
contrast to the periodic variation observed for periodic delay. Theoretical and
numerical results indicate that introducing a quasiperiodic delay modulation
into a time-delay system can lead to a giant reduction of the dimension of the
chaotic attractors. By varying the mean delay and keeping other parameters
fixed, we found that the Kaplan-Yorke dimension is modulated quasiperiodically
over several orders of magnitudes, where the dynamics switches
quasiperiodically between different types of high- and low-dimensional types of
chaos.Comment: 17 pages, 9 figure
Finite-time Stability, Dissipativity and Passivity Analysis of Discrete-time Neural Networks Time-varying Delays
The neural network time-varying delay was described as the dynamic properties of a neural cell, including neural functional and neural delay differential equations. The differential expression explains the derivative term of current and past state. The objective of this paper obtained the neural network time-varying delay. A delay-dependent condition is provided to ensure the considered discrete-time neural networks with time-varying delays to be finite-time stability, dissipativity, and passivity. This paper using a new Lyapunov-Krasovskii functional as well as the free-weighting matrix approach and a linear matrix inequality analysis (LMI) technique constructing to a novel sufficient criterion on finite-time stability, dissipativity, and passivity of the discrete-time neural networks with time-varying delays for improving. We propose sufficient conditions for discrete-time neural networks with time-varying delays. An effective LMI approach derives by base the appropriate type of Lyapunov functional. Finally, we present the effectiveness of novel criteria of finite-time stability, dissipativity, and passivity condition of discrete-time neural networks with time-varying delays in the form of linear matrix inequality (LMI)
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