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In this work, we consider Discrete-Time Continuous-Space Dynamic Systems for which we study the computability of the standard semantics of CTL* (CTL, LTL) and provide a variant thereof computable in the sense of Type-2 Theory of Effectivity. In particular, we show how the computable model checking of existentially and universally quantified path formulae of LTL can be reduced to solving, respectively, repeated reachability and persistence problems on a model obtained as a parallel composition of the original one and a non-deterministic Büchi automaton corresponding to the verified LTL formula.

Epilepsy is a condition in which periods of ongoing normal EEG activity alternate with periods of oscillatory behavior characteristic of epileptic seizures. The dynamics of the transitions between the two states are still unclear. Computational models provide a powerful tool to explore the underlying mechanisms of such transitions, with the purpose of eventually finding therapeutic interventions for this debilitating condition. In this study, the possibility to postpone seizures elicited by a decrease of inhibition is investigated by using external stimulation in a realistic bistable neuronal model consisting of two interconnected neuronal populations representing pyramidal cells and interneurons. In the simulations, seizures are induced by slowly decreasing the conductivity of GABA${}_{\mathrm{\text{A}}}$ synaptic channels over time. Since the model is bistable, the system will change state from the initial steady state (SS) to the limit cycle (LS) state because of internal noise, when the inhibition falls below a certain threshold. Several state-independent stimulations paradigms are simulated. Their effectiveness is analyzed for various stimulation frequencies and intensities in combination with periodic and random stimulation sequences. The distributions of the time to first seizure in the presence of stimulation are compared with the situation without stimulation. In addition, stimulation protocols targeted to specific subsystems are applied with the objective of counteracting the baseline shift due to decreased inhibition in the system. Furthermore, an analytical model is used to investigate the effects of random noise. The relation between the strength of random noise stimulation, the control parameter of the system and the transitions between steady state and limit cycle are investigated. The study shows that it is possible to postpone epileptic activity by targeted stimulation in a realistic neuronal model featuring bistability and that it is possible to stop seizures by random noise in an analytical model.

In this paper we present a randomized uniform self-stabilizing protocol that provides each (anonymous) processor of a uniform system with a distinct identifier. The protocol uses a predefined fixed amount of memory and stabilizes within expected Θ(d) time, where d is the actual diameter of the network. The naming protocol can be combined with self-stabilizing protocols that assume distinct identifiers for the processors. Thus, we achieve with optimal time and predefined amount of memory uniform self-stabilizing protocols for many tasks including: Spanning tree construction, leader election and reset.

We analyze the stability of a class of thin-shell wormholes with spherical symmetry evolving in flat FRW spacetimes. The wormholes considered here are supported at the throat by a perfect fluid with equation of state and have a physical radius equal to aR, where a is a time-dependent function describing the dynamics of the throat and R is the background scale factor. The study of wormhole stability is done by means of the stability analysis of dynamic systems.

This paper presents some exponential function solutions of the (3+1)-dimensional space-time fractional modified KdV–Zakharov–Kuznetsov (mKdV–ZK). The improved Bernoulli sub-equation function method (IBSEFM) is used in carrying out this computation. Choosing the suitable parameters, the 2D and 3D surfaces of solutions are plotted. The constructed results may be useful in explaining the physical meaning of the studied model.

Unusual behavior of dynamic systems with a control parameter is analyzed. Bifurcation induced qualitative changes in phase portraits of such systems are quite routine and ensure efficient operation. This class of systems includes ships with high maneuvering capabilities, aircraft and controlled underwater vehicles designed to be unstable in steady-state motion that are interesting in terms of applications.

Bifurcations may generate tracks of bifurcation memory that are "indicators" of regions of reduced controllability referred to as phase spots. The transition process in the phase spot is estimated qualitatively as a universal dependence of the index of loss of controllability on the control parameter.

The proposed approach has allowed us to predict and investigate emergency manifestations of the bifurcation memory effect occurring during routine maneuvering.

In this paper, the axisymmetric flow of a viscous fluid through a porous annular tube with walls kept at different temperatures is studied theoretically. The physical properties of the fluid remain constant, notably its specific mass, its dynamic viscosity and its thermal diffusivity. The nondimensional parameters which the solutions of the problem depend on are defined. A numerical integration using the shooting method is applied for solving the Navier–Stokes equations and the energy equation. Bifurcation diagrams are presented and enable to highlight significant properties of the flow. Some thermal behaviors corresponding to specific values of the parameters are performed. Asymmetric solutions of the steady flow are described and some results about velocity components are also analyzed.

In this paper, we study HIV mathematical models with treatments. Two models with RT inhibitor and HIV protease inhibitor are studied. Local and global analysis is carried out. By identifying a critical number for both treatments, we show that if the treatment is at least effective, then the uninfected steady state P₀ is the only equilibrium in the feasible region, and P₀ is globally asymptotically stable. Therefore, no HIV infection persists and infected T cells and HIV virus are cleared over time. However, if the treatment is not effective enough, i.e. less than , then a unique infected steady state P* emerges in the interior of the feasible region. P₀ becomes unstable and the system is uniformly persistent. Therefore, HIV infection persists. In this case, the unique infected steady state can be either stable or unstable. We show that it is locally stable only for r (the proliferation rate of T cells) small or large and unstable for some intermediate values. Global stability result is established for small values of r. Numerical simulation shows that once P* becomes unstable, periodic solution appears.

The mechanistic model of a dynamic system is often so complex that it is not conducive to probability-based design optimization. This is so because the common method to evaluate probability is the Monte Carlo method which requires thousands of lifetime simulations to provide probability distributions. This paper presents a methodology that (1) replaces the implicit mechanistic model with a simple explicit model, and (2), transforms the dynamic, probabilistic, problem into a time invariant probability problem. Probabilities may be evaluated by any convenient method, although the first-order reliability method is particularly attractive because of its speed and accuracy. A part of the methodology invokes design of computer experiments and approximating functions. Training sets of the design variables are selected, a few computer experiments are run to produce a matrix of corresponding responses at discrete times, and then the matrix is replaced with a vector of so-called metamodels. Responses at an arbitrary design set and at any time are easily calculated and then used to formulate common, time-invariant, performance measures. Design variables are treated as random variables and limit-state functions are formed in standard normal probability space. Probability-based design is now straightforward and optimization determines the best set of distribution parameters. Systems reliability methods may be invoked for multiple competing performance measures. Further, singular value decomposition may be used to reduce greatly the number of metamodels needed by transforming the response matrix into two smaller matrices: One containing the design variable-specific information and the other the time-specific information. An error analysis is presented. A case study of a servo-control mechanism shows the new methodology provides controllable accuracy and a substantial time reduction when compared to the traditional mechanistic model with Monte Carlo sampling.

The stability of dynamic systems is important for satisfactory performance, safety and reliability. The study becomes more difficult when the system is nonlinear and when the ever present uncertainties in the components are considered. Herein a new approach is presented that uses time-domain information: It invokes design of experiments based on the uncertainty within the system, computer simulation of the dynamics to generate a matrix of discrete time responses that presents the variability of the response, and finally, singular value decomposition to separate out parameter information from time information. The variability in the elements in the first few left singular vectors predicts any instability that might occur over the complete life-time of the system. The key to the approach is the introduction of random variables and subsequent co-variance operations. A real-world example and comparison to established methods show the efficacy of the approach.

In the inverse problem, it is common that either the corresponding component parameters or the corresponding input signals are obtained for a given output or response. Most model-based solutions to the inverse problem involve optimization using the so-called forward model. The forward model typically comprises the mechanistic model in some form. Most commonly, inverse problems are formulated in a static setting where a wealth of theoretical results and numerical methods are available. However, there are many important dynamic applications wherein time-dependent information needs to be discerned from time-dependent data. Recently, data-based approaches, or model-free methods, have been invoked whereby feature extraction methods such as Support vector machines (SVM) and artificial neural networks (ANN) are used. Herein we develop an inverse solution for dynamic systems through easy-to-understand least-squares meta-model mathematics. The input and output training data are interchanged, so that a mixed input comprising both component parameters and discrete-time excitations can be found for a given discrete-time output. Single-value decomposition (SVD) makes any matrix inversion tractable. The inverse meta-model is compared to the optimization method and ANN using mechanistic models for fidelity, and is shown to have better accuracy and much increased speed.

This paper introduces a novel approach for contour-based shape matching named as Constructive Relaxation Matching (CRM). Relaxation Matching (RM) introduced by Rosenfeld et al. is one of the standard method for quasi-optimally solving the local correspondences of the template and input images. RM relies on an energy-minimizing nature of the dynamical system to update the label assignment to the input objects. In image matching relying on a particular modeling method, apparently similar images can be judged as being quite distant, according to the nature of the modeling process and its outcome. In the proposed CRM, the modeling stage of a novel input image contour, conventionally done in the same procedure used for modeling the templates, will be included in the procedure of iterative relaxation matching. The model of the input will be dynamically constructed during relaxation, by unifying the pairs of objects having similar template label assignment probabilities. After describing the CRM procedures, the method is applied to simple shape matching problems demonstrating the ability to adaptively model the input image during relaxation. It is shown that the proposed CRM improves the object-label correspondence for evaluation of the image similarities in the following stages of shape matching applications.

The aim of this research is develop an effective virtual prototyping system for product development using augmented reality technology. Before a virtual environment is put into work for design and development, some way of quantifying errors or uncertainties in the computer model is needed so that a robust and reliable system can be achieved. This paper presents the calibration, registration, and preparation of an augmented reality environment with 3D tracking and dynamic simulation technologies for studying dynamic systems, such as parts orientation devices. With such virtual prototyping techniques, engineers can run high-fidelity simulation to test new materials, components, and systems before investing valuable resources in construction of physical prototypes.

In this study, we revisit the well-known notion of fuzzy state machines and discuss their development through learning. The systematic development of fuzzy state machines has not been pursued as intensively as it could have been expected from the breadth of the possible usage of them as various modelling platforms. We concentrate on the generalization of the well known architectures exploited in Boolean system synthesis, namely Moore and Mealy machines and show how these can be implemented in terms of generic functional modules such as fuzzy JK flip-flops and fuzzy logic neurons (AND and OR neurons) organized in the form of logic processors. It is shown that the design of the fuzzy state machines can be accomplished through their learning. The detailed learning algorithm is presented and illustrated with a series of numeric examples. The study reveals an interesting option of constructing digital systems through learning: the original problem is solved in the setting of fuzzy state machines and afterwards "binarised" into the two-valued format realized via the standard digital hardware.

We describe a novel affect-inspired mechanism to improve the performance of computational systems operating in dynamic environments. In particular, we designed a mechanism that is based on aspects of the fear response in humans to dynamically reallocate operating system-level central processing unit (CPU) resources to processes as they are needed to deal with time-critical events. We evaluated this system in the MINIX^® and Linux^® operating systems and in three different testing environments (two simulated, one live). We found the affect-based system was not only able to react more rapidly to time-critical events as intended, but since the dynamic processes for handling these events did not need to use significant CPU when they were not in time-critical situations, our simulated unmanned aerial vehicle (UAV) was able to perform even non-emergency tasks at a higher level of efficiency and reactivity than was possible in the standard implementation.

In This paper, a mixed robust sliding mode with fuzzy logic controller is applied to a nonlinear quadrotor Unmanned Aerial Vehicle (UAV). Based on the technique of variable structure control (VSC) with sliding mode, we can construct the controller that possesses the merits of both fuzzy Logic Controller (FLC) and Sliding Mode Controller (SMC), It is called a Fuzzy Sliding Mode Controller (FSMC). It provides a simple way to solve the main drawback of VSC by reducing the amount of chattering effect using a fuzzy control part in the proposed controller. Also, the VSC part makes the system stable which treats the main disadvantage of fuzzy controller when being used alone. Numerical simulation of the proposed controller is presented and discussed. Furthermore, a comparison with the SMC is also made.