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Nonlinear dynamics

Joshua Kiddy K Asamoah, Farai Nyabadza, Baba Seidu, Mehar Chand, Hemen Dutta
Vaccination and treatment are the most effective ways of controlling the transmission of most infectious diseases. While vaccination helps susceptible individuals to build either a long-term immunity or short-term immunity, treatment reduces the number of disease-induced deaths and the number of infectious individuals in a community/nation. In this paper, a nonlinear deterministic model with time-dependent controls has been proposed to describe the dynamics of bacterial meningitis in a population. The model is shown to exhibit a unique globally asymptotically stable disease-free equilibrium ℰ 0 , when the effective reproduction number ℛ VT ≤ 1, and a globally asymptotically stable endemic equilibrium ℰ 1 , when ℛ VT > 1; and it exhibits a transcritical bifurcation at ℛ VT = 1...
2018: Computational and Mathematical Methods in Medicine
Adora M DSouza, Anas Z Abidin, Udaysankar Chockanathan, Giovanni Schifitto, Axel Wismüller
Functional connectivity analysis of functional MRI (fMRI) can represent brain networks and reveal insights into interactions amongst different brain regions. However, most connectivity analysis approaches adopted in practice are linear and non-directional. In this paper, we demonstrate the advantage of a data-driven, directed connectivity analysis approach called Mutual Connectivity Analysis using Local Models (MCA-LM) that approximates connectivity by modeling nonlinear dependencies of signal interaction, over more conventionally used approaches, such as Pearson's and partial correlation, Patel's conditional dependence measures, etcetera...
May 16, 2018: NeuroImage
Hongjun Choi, Mingi Kim, Onseok Lee
Animal tracking is an important tool for observing behavior, which is useful in various research areas. Animal specimens can be tracked using dynamic models and observation models that require several types of data. Tracking mouse has several barriers due to the physical characteristics of the mouse, their unpredictable movement, and cluttered environments. Therefore, we propose a reliable method that uses a detection stage and a tracking stage to successfully track mouse. The detection stage detects the surface area of the mouse skin, and the tracking stage implements an extended Kalman filter to estimate the state variables of a nonlinear model...
May 19, 2018: Medical & Biological Engineering & Computing
Rinku Roy, Debdeep Sikdar, Manjunatha Mahadevappa, C S Kumar
A stable grasp is attained through appropriate hand preshaping and precise fingertip forces. Here, we have proposed a method to decode grasp patterns from motor imagery and subsequent fingertip force estimation model with a slippage avoidance strategy. We have developed a feature-based classification of electroencephalography (EEG) associated with imagination of the grasping postures. Chaotic behaviour of EEG for different grasping patterns has been utilised to capture the dynamics of associated motor activities...
May 19, 2018: Medical & Biological Engineering & Computing
Hanyuan Zhang, Xuemin Tian, Xiaogang Deng, Yuping Cao
As an attractive nonlinear dynamic data analysis tool, global preserving kernel slow feature analysis (GKSFA) has achieved great success in extracting the high nonlinearity and inherently time-varying dynamics of batch process. However, GKSFA is an unsupervised feature extraction method and lacks the ability to utilize batch process class label information, which may not offer the most effective means for dealing with batch process monitoring. To overcome this problem, we propose a novel batch process monitoring method based on the modified GKSFA, referred to as discriminant global preserving kernel slow feature analysis (DGKSFA), by closely integrating discriminant analysis and GKSFA...
May 16, 2018: ISA Transactions
Andreas Brechtel, Philipp Gramlich, Daniel Ritterskamp, Barbara Drossel, Thilo Gross
We study diffusion-driven pattern formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space...
March 2018: Physical Review. E
Reimar H Leike, Torsten A Enßlin
Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data providing information about a real physical field that is unknown. This information is sought to be conserved by the scheme as the field evolves in time. Such an information theoretic approach to simulation was pursued before by information field dynamics (IFD). In this paper we work out the theory of IFD for nonlinear PDEs in a noiseless Gaussian approximation...
March 2018: Physical Review. E
Sunil Kumar Yadav, Shankar P Das
Starting from a microscopic model, the continuum field theoretic description of the dynamics of a system of active ingredients or "particles" is presented. The equations of motion for the respective collective densities of mass and momentum follow exactly from that of a single element in the flock. The single-particle dynamics has noise and anomalous momentum dependence in its frictional terms. The equations for the collective densities are averaged over a local equilibrium distribution to obtain the corresponding coarse grained equations of fluctuating nonlinear hydrodynamics (FNH)...
March 2018: Physical Review. E
Kumari Priti Sinha, Rochish M Thaokar
Vesicles or biological cells under simultaneous shear and electric field can be encountered in dielectrophoretic devices or designs used for continuous flow electrofusion or electroporation. In this work, the dynamics of a vesicle subjected to simultaneous shear and uniform alternating current (ac) electric field is investigated in the small deformation limit. The coupled equations for vesicle orientation and shape evolution are derived theoretically, and the resulting nonlinear equations are handled numerically to generate relevant phase diagrams that demonstrate the effect of electrical parameters on the different dynamical regimes such as tank treading (TT), vacillating breathing (VB) [called trembling (TR) in this work], and tumbling (TU)...
March 2018: Physical Review. E
Marco Lauricella, Simone Melchionna, Andrea Montessori, Dario Pisignano, Giuseppe Pontrelli, Sauro Succi
We present a lattice Boltzmann model for charged leaky dielectric multiphase fluids in the context of electrified jet simulations, which are of interest for a number of production technologies including electrospinning. The role of nonlinear rheology on the dynamics of electrified jets is considered by exploiting the Carreau model for pseudoplastic fluids. We report exploratory simulations of charged droplets at rest and under a constant electric field, and we provide results for charged jet formation under electrospinning conditions...
March 2018: Physical Review. E
Urna Basu, Laurent Helden, Matthias Krüger
Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many-body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse-grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far-from-equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many-body systems...
May 4, 2018: Physical Review Letters
Weinan Gao, Zhong-Ping Jiang
This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods...
June 2018: IEEE Transactions on Neural Networks and Learning Systems
Bo Fan, Qinmin Yang, Xiaoyu Tang, Youxian Sun
In this paper, a novel robust adaptive dynamic programming (RADP)-based control strategy is presented for the optimal control of a class of output-constrained continuous-time unknown nonlinear systems. Our contribution includes a step forward beyond the usual optimal control result to show that the output of the plant is always within user-defined bounds. To achieve the new results, an error transformation technique is first established to generate an equivalent nonlinear system, whose asymptotic stability guarantees both the asymptotic stability and the satisfaction of the output restriction of the original system...
June 2018: IEEE Transactions on Neural Networks and Learning Systems
Huaguang Zhang, Qiuxia Qu, Geyang Xiao, Yang Cui
Based on integral sliding mode and approximate dynamic programming (ADP) theory, a novel optimal guaranteed cost sliding mode control is designed for constrained-input nonlinear systems with matched and unmatched disturbances. When the system moves on the sliding surface, the optimal guaranteed cost control problem of sliding mode dynamics is transformed into the optimal control problem of a reformulated auxiliary system with a modified cost function. The ADP algorithm based on single critic neural network (NN) is applied to obtain the approximate optimal control law for the auxiliary system...
June 2018: IEEE Transactions on Neural Networks and Learning Systems
Georgios D Sideridis, Panagiotis Simos, Angeliki Mouzaki, Dimitrios Stamovlasis, George K Georgiou
The purpose of the present study was to explain the moderating role of rapid automatized naming (RAN) in word reading with a cusp catastrophe model. We hypothesized that increases in RAN performance speed beyond a critical point would be associated with the disruption in word reading, consistent with a "generic shutdown" hypothesis. Participants were 587 elementary schoolchildren (Grades 2-4), among whom 87 had reading comprehension difficulties per the IQ-achievement discrepancy criterion. Data were analyzed via a cusp catastrophe model derived from the nonlinear dynamics systems theory...
May 1, 2018: Journal of Learning Disabilities
Bei Ding, Lijiang Yang, Debopreeti Mukherjee, Jianxin Chen, Yi Qin Gao, Feng Gai
: We employ site-specific, linear and nonlinear infrared spectroscopic techniques as well as fluorescence spectroscopy and molecular dynamics simulations to investigate the binding interactions of urea and three of its derivatives, methylurea, 1,3-dimethylurea and tetramethylurea, with protein aromatic and polar sidechains. We find that (1) urea methylation leads to preferential interactions between the co-solvent molecules and aromatic sidechains with an affinity that increases with the number of methyl groups; (2) interactions with tetramethylurea cause significant dehydration of aromatic sidechains and the effect is most pronounced for tryptophan; and (3) while neither urea nor tetramethylurea shows preferential accumulation around a polar sidechain, the number of hydrogen-bond donors around this sidechain is significantly decreased in the presence of tetramethylurea...
May 16, 2018: Journal of Physical Chemistry Letters
Yi Yang, Xiaofeng Liao, Tao Dong
Recently, the hybrid neuron models which combine the basic neuron models with impulsive effect(the state reset process) had been proposed, however, the preset value and the reset value of membrane potential were both fixed constants in the known models. In this paper, the Hindmarsh-Rose neuron model with nonlinear reset process is presented where the preset value and the reset value of membrane potential are variable constants. We conduct a qualitative analysis in the vicinity of the equilibrium point or the limit cycle of the proposed system by using the theories of impulsive semi-dynamical systems...
April 27, 2018: Neural Networks: the Official Journal of the International Neural Network Society
Fabio Cecconi, Andrea Puglisi, Alessandro Sarracino, Angelo Vulpiani
We study, via extensive numerical simulations, the force-velocity
 curve of an active particle advected by a steady laminar flow, in the
 nonlinear response regime. Our model for an active particle relies on
 a colored noise term that mimics its persistent motion over a time
 scale τ<sub>Α</sub>. We find that the active particle dynamics shows
 non-trivial effects, such as negative differential and absolute
 mobility (NDM and ANM, respectively)...
May 15, 2018: Journal of Physics. Condensed Matter: An Institute of Physics Journal
V Achilleos, G Theocharis, Ch Skokos
We investigate the dynamics of highly polydisperse finite granular chains. From the spatiospectral properties of small vibrations, we identify which particular single-particle displacements lead to energy localization. Then, we address a fundamental question: Do granular nonlinearities and the resulting chaotic dynamics destroy this energy localization? Our numerical simulations show that for moderate nonlinearities, the overall system behaves chaotically, and spreading of energy occurs. However, long-lasting chaotic energy localization is observed for particular single-particle excitations in the presence of the nonsmooth nonlinearities...
April 2018: Physical Review. E
Juan D Bernal, Jesús M Seoane, Miguel A F Sanjuán
Chaotic scattering is an important topic in nonlinear dynamics and chaos with applications in several fields in physics and engineering. The study of this phenomenon in relativistic systems has received little attention as compared to the Newtonian case. Here we focus our work on the study of some relevant characteristics of the exit basin topology in the relativistic Hénon-Heiles system: the uncertainty dimension, the Wada property, and the basin entropy. Our main findings for the uncertainty dimension show two different behaviors insofar as we change the relativistic parameter β, in which a crossover behavior is uncovered...
April 2018: Physical Review. E
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