SCIENCEGATE

NONLINEAR ANALYSIS MODELLING AND CONTROL

Publisher:
vilnius university
ISSN(s):
1392-5113  1392-5113  
Last Update Time:
January 11, 2021
Total Documents:
805
Top Keywords:
Differential Equations
Fixed Point
Mathematical Model
Boundary Conditions
Differential Equation
Finite Difference
Neural Networks
Fractional Differential
Theoretical Results
Heat Transfer
Boundary Value
Hopf Bifurcation
Metric Spaces
Steady State
Numerical Simulations
Fixed Point Theorems
Boundary Value Problem
Positive Solutions
Mass Transfer
Fixed Point Theorem

The issue of quantized passive filtering for switched delayed neural networks with noise interference is studied in this paper. Both arbitrary and semi-Markov switching rules are taken into account. By choosing Lyapunov functionals and applying several inequality techniques, sufficient conditions are proposed to ensure the filter error system to be not only exponentially stable, but also exponentially passive from the noise interference to the output error. The gain matrix for the proposed quantized passive filter is able to be determined through the feasible solution of linear matrix inequalities, which are computationally tractable with the help of some popular convex optimization tools. Finally, two numerical examples are given to illustrate the usefulness of the quantized passive filter design methods.

Keywords:
neural networks ◽
convex optimization ◽
linear matrix inequalities ◽
feasible solution ◽
linear matrix ◽
lyapunov functionals ◽
passive filter ◽
delayed neural networks ◽
noise interference ◽
inequality techniques

In this paper, we consider an improved Human T-lymphotropic virus type I (HTLV-I) infection model with the mitosis of CD4+ T cells and delayed cytotoxic T-lymphocyte (CTL) immune response by analyzing the distributions of roots of the corresponding characteristic equations, the local stability of the infection-free equilibrium, the immunity-inactivated equilibrium, and the immunity-activated equilibrium when the CTL immune delay is zero is established. And we discuss the existence of Hopf bifurcation at the immunity-activated equilibrium. We define the immune-inactivated reproduction ratio R0 and the immune-activated reproduction ratio R1. By using Lyapunov functionals and LaSalle’s invariance principle, it is shown that if R0 < 1, the infection-free equilibrium is globally asymptotically stable; if R1 < 1 < R0, the immunity-inactivated equilibrium is globally asymptotically stable; if R1 > 1, the immunity-activated equilibrium is globally asymptotically stable when the CTL immune delay is zero. Besides, uniform persistence is obtained when R1 > 1. Numerical simulations are carried out to illustrate the theoretical results.

Keywords:
immune response ◽
t cells ◽
hopf bifurcation ◽
cd4 t cells ◽
infection model ◽
asymptotically stable ◽
globally asymptotically stable ◽
reproduction ratio ◽
ctl immune response ◽
theoretical results

In this paper, we introduce a generalization of the squared remainder minimization method for solving multi-term fractional differential equations. We restrict our attention to linear equations. Approximate solutions of these equations are considered in terms of linearly independent functions. We change our problem into a minimization problem. Finally, the Lagrange-multiplier method is used to minimize the resultant problem. The convergence of this approach is discussed and theoretically investigated. Some relevant examples are investigated to illustrate the accuracy of the method, and obtained results are compared with other methods to show the power of applied method.

Keywords:
differential equations ◽
lagrange multiplier ◽
fractional differential equations ◽
minimization problem ◽
linear equations ◽
approximate solutions ◽
multiplier method ◽
minimization method ◽
independent functions ◽
fractional differential

In this paper, we consider a diffusive predator–prey system with strong Allee effect and two delays. First, we explore the stability region of the positive constant steady state by calculating the stability switching curves. Then we derive the Hopf and double Hopf bifurcation theorem via the crossing directions of the stability switching curves. Moreover, we calculate the normal forms near the double Hopf singularities by taking two delays as parameters. We carry out some numerical simulations for illustrating the theoretical results. Both theoretical analysis and numerical simulation show that the system near double Hopf singularity has rich dynamics, including stable spatially homogeneous and inhomogeneous periodic solutions. Finally, we evaluate the influence of two parameters on the existence of double Hopf bifurcation.

Keywords:
hopf bifurcation ◽
allee effect ◽
double hopf bifurcation ◽
predator prey ◽
prey system ◽
spatially homogeneous ◽
strong allee effect ◽
two delays ◽
theoretical results ◽
the stability

In this paper, we adopt D-type and PD-type learning laws with the initial state of iteration to achieve uniform tracking problem of multi-agent systems subjected to impulsive input. For the multi-agent system with impulse, we show that all agents are driven to achieve a given asymptotical consensus as the iteration number increases via the proposed learning laws if the virtual leader has a path to any follower agent. Finally, an example is illustrated to verify the effectiveness by tracking a continuous or piecewise continuous desired trajectory.

Keywords:
iterative learning control ◽
iterative learning ◽
multi agent system ◽
tracking problem ◽
multi agent systems ◽
initial state ◽
agent systems ◽
piecewise continuous ◽
iteration number ◽
multi agent

In this paper, the projective synchronization of BAM neural networks with time-varying delays is studied. Firstly, a type of novel adaptive controller is introduced for the considered neural networks, which can achieve projective synchronization. Then, based on the adaptive controller, some novel and useful conditions are obtained to ensure the projective synchronization of considered neural networks. To our knowledge, different from other forms of synchronization, projective synchronization is more suitable to clearly represent the nonlinear systems’ fragile nature. Besides, we solve the projective synchronization problem between two different chaotic BAM neural networks, while most of the existing works only concerned with the projective synchronization chaotic systems with the same topologies. Compared with the controllers in previous papers, the designed controllers in this paper do not require any activation functions during the application process. Finally, an example is provided to show the effectiveness of the theoretical results.

Keywords:
neural networks ◽
nonlinear systems ◽
chaotic systems ◽
adaptive controller ◽
projective synchronization ◽
time varying ◽
bam neural networks ◽
activation functions ◽
varying delay ◽
theoretical results

In this paper, we introduce the concept of cyclic p-contraction pair for single-valued mappings. Then we present some best proximity point results for such mappings defined on proximally complete pair of subsets of a metric space. Also, we provide some illustrative examples that compared our results with some earliest. Finally, by taking into account a fixed point consequence of our main result we give an existence and uniqueness result for a common solution of a system of second order boundary value problems.

Keywords:
fixed point ◽
boundary value problems ◽
metric space ◽
existence and uniqueness ◽
best proximity point ◽
boundary value ◽
uniqueness result ◽
second order ◽
common solution

We present a possible kind of generalization of the notion of ordered pairs of cyclic maps and coupled fixed points and its application in modelling of equilibrium in oligopoly markets. We have obtained sufficient conditions for the existence and uniqueness of coupled fixed in complete metric spaces. We illustrate one possible application of the results by building a pragmatic model on competition in oligopoly markets. To achieve this goal, we use an approach based on studying the response functions of each market participant, thus making it possible to address both Cournot and Bertrand industrial structures with unified formal method.We show that whenever the response functions of the two players are identical, then the equilibrium will be attained at equal levels of production and equal prices. The response functions approach makes it also possible to take into consideration different barriers to entry. By fitting to the response functions rather than the profit maximization of the payoff functions problem we alter the classical optimization problem to a problem of coupled fixed points, which has the benefit that considering corner optimum, corner equilibrium and convexity condition of the payoff function can be skipped.

Keywords:
variational principle ◽
fixed points ◽
existence and uniqueness ◽
optimization problem ◽
response functions ◽
oligopoly markets ◽
payoff functions ◽
ordered pairs ◽
classical optimization ◽
coupled fixed points

In this paper, we study a time-periodic model, which incorporates seasonality and host stage-structure. This model describes the propagation of Puumala hantavirus within the bank vole population of Clethrionomys glareolus. The basic reproduction number R0 is obtained. By appealing to the theory of monotone dynamical systems and chain transitive sets, we establish a threshold-type result on the global dynamics in terms of R0, that is, the virus-free periodic solution is globally attractive, and the virus dies out if R0 ≤ 1, while there exists a unique positive periodic solution, which is globally attractive, and the virus persists if R0 > 1. Numerical simulations are given to confirm our theoretical results and to show that cleaning environment and controlling the grow of mice population are essential control strategies to reduce hantavirus infection.

Keywords:
periodic solution ◽
dynamical systems ◽
hantavirus infection ◽
global dynamics ◽
monotone dynamical systems ◽
time periodic ◽
chain transitive sets ◽
the basic reproduction number ◽
theoretical results ◽
globally attractive

We investigate the existence of positive solutions for a nonlinear Riemann–Liouville fractional differential equation with a positive parameter subject to nonlocal boundary conditions, which contain fractional derivatives and Riemann–Stieltjes integrals. The nonlinearity of the equation is nonnegative, and it may have singularities at its variables. In the proof of the main results, we use the fixed point index theory and the principal characteristic value of an associated linear operator. A related semipositone problem is also studied by using the Guo–Krasnosel’skii fixed point theorem.

Keywords:
differential equation ◽
fixed point ◽
fixed point theorem ◽
linear operator ◽
boundary value problem ◽
boundary conditions ◽
fractional differential equation ◽
positive solutions ◽
fixed point index theory ◽
fractional differential