Geostatistical Kriging is performed on hydrologic model parameters in a two-dimensional region—different from the geographical space—as a hydrospace. The x-axis in percent is a relative difference of soil characteri...Geostatistical Kriging is performed on hydrologic model parameters in a two-dimensional region—different from the geographical space—as a hydrospace. The x-axis in percent is a relative difference of soil characteristics between an embedded 12 watersheds in reference to a large one related to the Niger River in West Africa;noted var_WHC, it stands for Water Holding Capacity. The y-axis in percent, var_Nash, is a hydrologic model’s efficiency in two contexts: (a) calibrated model parameters on the reference watershed are injected in modelling on each sub-watershed in validation phase to produce a series of Nash values as references, (b) a second series of Nash values is produced in calibrations. SimulHyd which stands for Simulation of Hydrological Systems is applied along with a French hydrological model—Genie Rural with 2 parameters at Monthly time step. The built Nash-WHC hydrospace and its two variants, or hybrids, permit the krige of both hydrologic model’s parameters. The relative variation of upper module absolute ranges from 0.1% to 15.68%—the developed hydro-geostatistics practice is considered in reference to hydrological calibration. Accepted as hydrogeostatistics practice, it is applicable to ungauged watersheds to estimate hydrologic models’ parameters.展开更多
In this paper, the dynamical properties of Smith type diffusion model with Dirichlet boundary conditions are studied. The properties of hyperbolic fixed points and non-hyperbolic fixed points of the model are analyzed...In this paper, the dynamical properties of Smith type diffusion model with Dirichlet boundary conditions are studied. The properties of hyperbolic fixed points and non-hyperbolic fixed points of the model are analyzed. By using the central manifold theorem, the bifurcation phenomenon of the model is studied. The results show that flip, transcritical, pitchfork and Fold-flip bifurcations exist at non-hyperbolic fixed points.展开更多
Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of fi...Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of finite dimensional complex-valued systems with impulsive control fields, where the studied complex-valued systems are governed by the Schrödinger equation and can be used in quantum systems. By one Lyapunov function based on state error and the invariant principle of impulsive systems, I study the convergence of complex-valued systems with impulsive control fields and propose new results for the mentioned complex-valued systems in the form of sufficient conditions. A numerical simulation to validate the proposed control method is provided.展开更多
The DDE-Biftool software is applied to solve the dynamical stability and bifurcation problem of the neutrophil cells model. Based on Hopf point finding with the stability property of the equilibrium solution loss, the...The DDE-Biftool software is applied to solve the dynamical stability and bifurcation problem of the neutrophil cells model. Based on Hopf point finding with the stability property of the equilibrium solution loss, the continuation of the bifurcating periodical solution starting from Hopf point is exploited. The generalized Hopf point is tracked by seeking for the critical value of free parameter of the switching phenomena of the open loop, which describes the lineup of bifurcating periodical solutions from Hopf point. The normal form near the generalized Hopf point is computed by Lyapunov-Schimdt reduction scheme combined with the center manifold analytical technique. The near dynamics is classified by geometrically different topological phase portraits.展开更多
This work predicts theoretically the phase portrait including the existence and uniqueness of ω-limit cycle for an initial value problem y(0)=y0with an ordinary differential equation y′+py=fin which p and f are L-pe...This work predicts theoretically the phase portrait including the existence and uniqueness of ω-limit cycle for an initial value problem y(0)=y0with an ordinary differential equation y′+py=fin which p and f are L-periodic piecewise continuous functions.展开更多
In this paper, we investigate the existence of random attractor for the random dynamical system generated by the Kirchhoff-type suspension bridge equations with strong damping and white noises. We first prove the exis...In this paper, we investigate the existence of random attractor for the random dynamical system generated by the Kirchhoff-type suspension bridge equations with strong damping and white noises. We first prove the existence and uniqueness of solutions to the initial boundary value conditions, and then we study the existence of the global attractors of the equation.展开更多
In this paper we study the asymptotic dynamics of the stochastic strongly damped wave equation with multiplicative noise under homogeneous Dirichlet boundary condition. We investigate the existence of a compact random...In this paper we study the asymptotic dynamics of the stochastic strongly damped wave equation with multiplicative noise under homogeneous Dirichlet boundary condition. We investigate the existence of a compact random attractor for the random dynamical system associated with the equation.展开更多
In this paper, we consider the stochastic higher-order Kirchhoff-type equation with nonlinear strongly dissipation and white noise. We first deal with random term by using Ornstein-Uhlenbeck process and establish the ...In this paper, we consider the stochastic higher-order Kirchhoff-type equation with nonlinear strongly dissipation and white noise. We first deal with random term by using Ornstein-Uhlenbeck process and establish the wellness of the solution, then the existence of global random attractor are proved.展开更多
In this paper, firstly, some priori estimates are obtained for the existence and uniqueness of solutions of a two dimensional generalized anisotropy Kuramoto-Sivashinsky Equation. Then we prove the existence of the gl...In this paper, firstly, some priori estimates are obtained for the existence and uniqueness of solutions of a two dimensional generalized anisotropy Kuramoto-Sivashinsky Equation. Then we prove the existence of the global attractor. Finally, we get the upper bound estimation of the Haus-dorff and fractal dimension of attractor.展开更多
In this paper Nottale’s acclaimed scale relativity theory is given a transfinite Occam’s razor leading to exact predictions of the missing dark energy [1,2] of the cosmos. It is found that 95.4915% of the energy in ...In this paper Nottale’s acclaimed scale relativity theory is given a transfinite Occam’s razor leading to exact predictions of the missing dark energy [1,2] of the cosmos. It is found that 95.4915% of the energy in the cosmos according to Einstein’s prediction must be dark energy or not there at all. This percentage is in almost complete agreement with actual measurements.展开更多
In this article, we prove the existence of exponential attractors of the nonclassical diffusion equation with critical nonlinearity and lower regular forcing term. As an additional product, we show that the fractal di...In this article, we prove the existence of exponential attractors of the nonclassical diffusion equation with critical nonlinearity and lower regular forcing term. As an additional product, we show that the fractal dimension of the global attractors of this problem is finite.展开更多
This paper considers the long-time behavior for a system of coupled wave equations of higher-order Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of t...This paper considers the long-time behavior for a system of coupled wave equations of higher-order Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of the inertial manifold while such equations satisfy the spectral interval condition.展开更多
This paper presents a voltage controller for a 12/8 switched reluctance generator (SRG). SR machines have a robust with simple structure because they have no windings or permanent magnets on the rotor, so they are cap...This paper presents a voltage controller for a 12/8 switched reluctance generator (SRG). SR machines have a robust with simple structure because they have no windings or permanent magnets on the rotor, so they are capable of working at high speed application and at rough condition. However, due to nonlinear nature, doubly salient poles, time variant parameters, and non-ideal current waveform, The SRG output voltage inherently contains ripples. The proposed voltage controller is based on fuzzy logic that is very efficient over uncertainty and parameter variations. The effectiveness of the proposed control method is verified by comparing the obtained result with that of a PI-controller.展开更多
The state reconstruction problem is addressed for complex dynamical networks coupled with states and outputs respectively, in a noisy transmission channel. By using Lyapunov stability theory and H∞ performance, two s...The state reconstruction problem is addressed for complex dynamical networks coupled with states and outputs respectively, in a noisy transmission channel. By using Lyapunov stability theory and H∞ performance, two schemes of state reconstruction are proposed for the complex dynamical networks with the nodes coupled by states and outputs respectively, and the estimation errors are convergent to zeros with H∞ performance index. A numerical simulation demonstrates the effectiveness of the proposed observers.展开更多
In the present paper, we prove some fixed point theorems of Hegedus contraction in some types of distance spaces, dislocated metric space, left dislocated metric space, right dislocated metric space and dislocated qua...In the present paper, we prove some fixed point theorems of Hegedus contraction in some types of distance spaces, dislocated metric space, left dislocated metric space, right dislocated metric space and dislocated quasi-metric metric space which are generalized metrics spaces where self-distances are not necessarily zero.展开更多
In this paper, we study the global and pullback attractors for a strongly damped wave equation with delays when the force term belongs to different space. The results following from the solution generate a compact set.
In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness o...In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.展开更多
In this paper, a class of discrete vertical and horizontal transmitted disease model under constant vaccination is researched. Under the hypothesis of population being constant size, the model is transformed into a pl...In this paper, a class of discrete vertical and horizontal transmitted disease model under constant vaccination is researched. Under the hypothesis of population being constant size, the model is transformed into a planar map and its equilibrium points and the corresponding eigenvalues are solved out. By discussing the influence of coefficient parameters on the eigenvalues, the hyperbolicity of equilibrium points is determined. By getting the equations of flows on center manifold, the direction and stability of the transcritical bifurcation and flip bifurcation are discussed.展开更多
Applying the modeling method of Grey system and accumulated generating operation of reciprocal number for the problem of lower precision as well as lower adaptability in non-equidistant GM (1, 1) model, the calculatio...Applying the modeling method of Grey system and accumulated generating operation of reciprocal number for the problem of lower precision as well as lower adaptability in non-equidistant GM (1, 1) model, the calculation formulas were deduced and a non-equidistant GRM (1, 1) model generated by accumulated generating operation of reciprocal number was put forward .The grey GRM (1, 1) model can be used in non-equal interval & equal interval time series and has the characteristic of high precision as well as high adaptability. Example validates the practicability and reliability of the proposed model.展开更多
文摘Geostatistical Kriging is performed on hydrologic model parameters in a two-dimensional region—different from the geographical space—as a hydrospace. The x-axis in percent is a relative difference of soil characteristics between an embedded 12 watersheds in reference to a large one related to the Niger River in West Africa;noted var_WHC, it stands for Water Holding Capacity. The y-axis in percent, var_Nash, is a hydrologic model’s efficiency in two contexts: (a) calibrated model parameters on the reference watershed are injected in modelling on each sub-watershed in validation phase to produce a series of Nash values as references, (b) a second series of Nash values is produced in calibrations. SimulHyd which stands for Simulation of Hydrological Systems is applied along with a French hydrological model—Genie Rural with 2 parameters at Monthly time step. The built Nash-WHC hydrospace and its two variants, or hybrids, permit the krige of both hydrologic model’s parameters. The relative variation of upper module absolute ranges from 0.1% to 15.68%—the developed hydro-geostatistics practice is considered in reference to hydrological calibration. Accepted as hydrogeostatistics practice, it is applicable to ungauged watersheds to estimate hydrologic models’ parameters.
文摘In this paper, the dynamical properties of Smith type diffusion model with Dirichlet boundary conditions are studied. The properties of hyperbolic fixed points and non-hyperbolic fixed points of the model are analyzed. By using the central manifold theorem, the bifurcation phenomenon of the model is studied. The results show that flip, transcritical, pitchfork and Fold-flip bifurcations exist at non-hyperbolic fixed points.
文摘Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of finite dimensional complex-valued systems with impulsive control fields, where the studied complex-valued systems are governed by the Schrödinger equation and can be used in quantum systems. By one Lyapunov function based on state error and the invariant principle of impulsive systems, I study the convergence of complex-valued systems with impulsive control fields and propose new results for the mentioned complex-valued systems in the form of sufficient conditions. A numerical simulation to validate the proposed control method is provided.
文摘The DDE-Biftool software is applied to solve the dynamical stability and bifurcation problem of the neutrophil cells model. Based on Hopf point finding with the stability property of the equilibrium solution loss, the continuation of the bifurcating periodical solution starting from Hopf point is exploited. The generalized Hopf point is tracked by seeking for the critical value of free parameter of the switching phenomena of the open loop, which describes the lineup of bifurcating periodical solutions from Hopf point. The normal form near the generalized Hopf point is computed by Lyapunov-Schimdt reduction scheme combined with the center manifold analytical technique. The near dynamics is classified by geometrically different topological phase portraits.
文摘This work predicts theoretically the phase portrait including the existence and uniqueness of ω-limit cycle for an initial value problem y(0)=y0with an ordinary differential equation y′+py=fin which p and f are L-periodic piecewise continuous functions.
文摘In this paper, we investigate the existence of random attractor for the random dynamical system generated by the Kirchhoff-type suspension bridge equations with strong damping and white noises. We first prove the existence and uniqueness of solutions to the initial boundary value conditions, and then we study the existence of the global attractors of the equation.
文摘In this paper we study the asymptotic dynamics of the stochastic strongly damped wave equation with multiplicative noise under homogeneous Dirichlet boundary condition. We investigate the existence of a compact random attractor for the random dynamical system associated with the equation.
文摘In this paper, we consider the stochastic higher-order Kirchhoff-type equation with nonlinear strongly dissipation and white noise. We first deal with random term by using Ornstein-Uhlenbeck process and establish the wellness of the solution, then the existence of global random attractor are proved.
文摘In this paper, firstly, some priori estimates are obtained for the existence and uniqueness of solutions of a two dimensional generalized anisotropy Kuramoto-Sivashinsky Equation. Then we prove the existence of the global attractor. Finally, we get the upper bound estimation of the Haus-dorff and fractal dimension of attractor.
文摘In this paper Nottale’s acclaimed scale relativity theory is given a transfinite Occam’s razor leading to exact predictions of the missing dark energy [1,2] of the cosmos. It is found that 95.4915% of the energy in the cosmos according to Einstein’s prediction must be dark energy or not there at all. This percentage is in almost complete agreement with actual measurements.
文摘In this article, we prove the existence of exponential attractors of the nonclassical diffusion equation with critical nonlinearity and lower regular forcing term. As an additional product, we show that the fractal dimension of the global attractors of this problem is finite.
文摘This paper considers the long-time behavior for a system of coupled wave equations of higher-order Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of the inertial manifold while such equations satisfy the spectral interval condition.
文摘This paper presents a voltage controller for a 12/8 switched reluctance generator (SRG). SR machines have a robust with simple structure because they have no windings or permanent magnets on the rotor, so they are capable of working at high speed application and at rough condition. However, due to nonlinear nature, doubly salient poles, time variant parameters, and non-ideal current waveform, The SRG output voltage inherently contains ripples. The proposed voltage controller is based on fuzzy logic that is very efficient over uncertainty and parameter variations. The effectiveness of the proposed control method is verified by comparing the obtained result with that of a PI-controller.
文摘The state reconstruction problem is addressed for complex dynamical networks coupled with states and outputs respectively, in a noisy transmission channel. By using Lyapunov stability theory and H∞ performance, two schemes of state reconstruction are proposed for the complex dynamical networks with the nodes coupled by states and outputs respectively, and the estimation errors are convergent to zeros with H∞ performance index. A numerical simulation demonstrates the effectiveness of the proposed observers.
文摘In the present paper, we prove some fixed point theorems of Hegedus contraction in some types of distance spaces, dislocated metric space, left dislocated metric space, right dislocated metric space and dislocated quasi-metric metric space which are generalized metrics spaces where self-distances are not necessarily zero.
文摘In this paper, we study the global and pullback attractors for a strongly damped wave equation with delays when the force term belongs to different space. The results following from the solution generate a compact set.
文摘In this paper, we study the longtime behavior of solution to the initial boundary value problem for a class of strongly damped Higher-order Kirchhoff type equations: . At first, we prove the existence and uniqueness of the solution by priori estimation and the Galerkin method. Then, we obtain to the existence of the global attractor. At last, we consider that the estimation of the upper bounds of Hausdorff and fractal dimensions for the global attractors are obtained.
文摘In this paper, a class of discrete vertical and horizontal transmitted disease model under constant vaccination is researched. Under the hypothesis of population being constant size, the model is transformed into a planar map and its equilibrium points and the corresponding eigenvalues are solved out. By discussing the influence of coefficient parameters on the eigenvalues, the hyperbolicity of equilibrium points is determined. By getting the equations of flows on center manifold, the direction and stability of the transcritical bifurcation and flip bifurcation are discussed.
文摘Applying the modeling method of Grey system and accumulated generating operation of reciprocal number for the problem of lower precision as well as lower adaptability in non-equidistant GM (1, 1) model, the calculation formulas were deduced and a non-equidistant GRM (1, 1) model generated by accumulated generating operation of reciprocal number was put forward .The grey GRM (1, 1) model can be used in non-equal interval & equal interval time series and has the characteristic of high precision as well as high adaptability. Example validates the practicability and reliability of the proposed model.
