Narrow Results

In the entire world, pneumonia is one of the leading causes of death, which is particularly dangerous for young children (those under five years old) and the elderly (those over 65). A deterministic susceptible, vaccinated, exposed, infected, and recovered (SVEIR) model is used in this work to mathematically study the dynamics of pneumonia disease and examine stability analysis, basic reproduction numbers, and equilibrium points of dynamical systems theory models. Spatial equilibria are studied to model disease-free equilibria that are locally asymptotic stable. Numerical simulations of the model have been carried out using MATLAB21. The SVEIR flow and its variables for different parameter sets have been studied through numerical simulations. The solution to the issue is provided through the use of illustrated and explicated results. According to research findings, if vaccination rates rise over the necessary vaccination ratio, the sickness will finally vanish from the community.

In most conventional complex network equilibrium-pinning control, all the network nodes are usually balanced by attaching at least one controller to each node of the concerned network. When the node number is huge and the inter-node connections are complex, this control strategy requires the ability to manipulate the inter-node coupling strength to grow rapidly and intensively. In practical applications, however, the inter-node coupling strength cannot be increased unlimitedly; as a matter of fact, the coupling strength cannot be further changed after reaching some saturation threshold. In this paper, by exploiting the improved coupling strength saturation function, we suggest a new pinning control strategy that makes the network reach its equilibrium-pinning point more effectively than the network with saturated coupling strength. Numerical examples are illustrated to show the effectiveness of the main results.

A modified continuum traffic flow model is established in this paper based on an extended car-following model considering driver’s reaction time and distance. The linear stability of the model and the Korteweg–de Vries (KdV) equation describing the density wave of traffic flow in the metastable region are obtained. In the new model, the relaxation term and the dissipation term exist at the same time, thus the type and stability of equilibrium solution of the model can be analyzed on the phase plane. Based on the equilibrium point, the bifurcation analysis of the model is carried out, and the existence of Hopf bifurcation and saddle-node bifurcation is proved. Numerical simulations show that the model can describe the complex nonlinear dynamic phenomena observed in freeway traffic, such as local cluster effect. Various bifurcations of the model, such as Hopf bifurcation, saddle-node bifurcation, Limit Point bifurcation of cycles, Cusp bifurcation and Bogdanov–Takens bifurcation, are also obtained by numerical simulations, and the traffic behaviors of some bifurcations are studied. The results show that the numerical solution is consistent with the analytical solution. Consequently, some nonlinear traffic phenomena can be analyzed and predicted from the perspective of global stability.

The stability of the transportation system refers to the structural stability of the system. When the system structure is unstable, local or global bifurcation phenomena will occur, which is one of the main reasons for nonlinear traffic phenomena such as congestion. To truly understand the internal mechanism of the formation of these phenomena, it is necessary to analyze the bifurcation of traffic flow. In this paper, the Hopf bifurcation control of a modified viscous macroscopic traffic flow model is studied by using the linear state feedback method, which changes the characteristics of the bifurcation phenomenon of the dynamic system and obtains the required dynamic behavior of the system. First, we can convert the original traffic model into the nonlinear ordinary differential form suitable for bifurcation analysis, solve the equilibrium point of the system, and carry out phase plane analysis. Then, the linear state feedback term is added and the corresponding controlled system is generated, the existence and type of Hopf bifurcation and the existence of saddle node bifurcation are proved. Numerical simulation results show that the analysis and control of Hopf bifurcation in the traffic model are well realized in this paper.

A dynamical system analysis related to Dirac–Born–Infeld (DBI) cosmological model has been investigated in this present work. For spatially flat FRW spacetime, the Einstein field equation for DBI scenario has been used to study the dynamics of DBI dark energy interacting with dark matter. The DBI dark energy model is considered as a scalar field with a nonstandard kinetic energy term. An interaction between the DBI dark energy and dark matter is considered through a phenomenological interaction between DBI scalar field and the dark matter fluid. The field equations are reduced to an autonomous dynamical system by a suitable redefinition of the basic variables. The potential of the DBI scalar field is assumed to be exponential. Finally, critical points are determined, their nature have been analyzed and corresponding cosmological scenario has been discussed.

This paper studies the problem of controlling the chaotic behavior of a modified coupled dynamos system. Two different methods, feedback and non-feedback methods, are used to control chaos in the modified coupled dynamos system. Based on the Lyapunov direct method and Routh–Hurwitz criterion, the conditions suppressing chaos to unstable equilibrium points or unstable periodic orbits (limit cycles) are discussed, and they are also proved theoretically. Numerical simulations show the effectiveness of the two different methods.

In this paper a chaotic system is proposed via modifying hyperchaotic Chen system. Some basic dynamical properties, such as Lyapunov exponents, fractal dimension, chaotic behaviors of this system are studied. The conventional feedback, linear function feedback, nonlinear hyperbolic function feedback control methods are applied to control chaos to unstable equilibrium point. The conditions of stability to control the system is derived according to the Routh–Hurwitz criteria. Numerical results have shown the validity of the proposed schemes.

In this paper, two different kinds of methods are adopted to control Liu system — feedback method and nonfeedback method. On the one hand, direct feedback and adaptive time-delayed feedback are taken as examples for the study of feedback control. In the direct feedback method, Liu system can be stabilized at one equilibrium point or a limit cycle surrounding its equilibrium. In the adaptive time-delayed feedback method, feedback coefficient and delay time can be adjusted adaptively to stabilize Liu system at its original unstable periodic orbit. On the other hand, periodic parametric perturbation is used to control chaos in Liu system as a typical nonfeedback method. By changing the frequency of the perturbation signal, Liu system can be guided to not only periodic motion but also hyperchaos. Numerical simulations show the effectiveness of our methods.

This paper addresses qualitative properties of equilibrium points in a class of delayed neural networks. We derive a sufficient condition for the local exponential stability of equilibrium points, and give an estimate on the domains of attraction of locally exponentially stable equilibrium points. Our condition and estimate are formulated in terms of the network parameters, the neurons' activation functions and the associated equilibrium point; hence, they are easily checkable. Another advantage of our results is that they neither depend on monotonicity of the activation functions nor on symmetry of the interconnection matrix. Our work has practical importance in evaluating the performance of the related associative memory. To our knowledge, this is the first time to present an estimate on the domains of attraction of equilibrium points for delayed neural networks.

In this paper, memory patterns of bidirectional associative memory (BAM) neural networks with time-delay are investigated based on stability theory. Several sufficient conditions are obtained such that the equilibrium point is locally exponentially stable when the point is located at the designated position. These conditions, which can be directly derived from the synaptic connection weights and the external input of the BAM neural networks, are very easy to be verified. In addition, three examples are given to show the effectiveness of the results.

In this paper, the global exponential stability of Chua's reaction–diffusion CNN system is investigated. For this system, some sufficient conditions ensuring the existence and global exponential stability of the equilibrium point is derived by using homeomorphism mapping, the property of coefficient matrix and analytical techniques. Finally, three illustrative examples are given to show the effectiveness of our results.

A simple approach for generating (2N + 1)-scroll chaotic attractor from a modified Colpitts oscillator model is proposed in this paper. The key strategy is to increase the number of index-2 equilibrium points by introducing a triangle function to directly replace the nonlinearity term of Colpitts oscillator model. The dynamical characteristics of the new multiscroll chaotic system are studied comprehensively. A circuit realization structure is introduced and the experimental results demonstrate that (2N + 1)-scroll chaotic attractors can be obtained in practical circuit.

The global exponential stability is studied for a class of high-order bi-directional associative memory (BAM) neural networks with time delays and reaction–diffusion terms. By constructing suitable Lyapunov functional, using differential mean value theorem and homeomorphism, several sufficient conditions guaranteeing the existence, uniqueness and global exponential stability of high-order BAM neural networks with time delays and reaction–diffusion terms are given. Two illustrative examples are also given in the end to show the effectiveness of our results.

In this paper, we consider a class of planar continuous piecewise linear vector fields with three zones. Using the Poincaré map, we show that these systems admit always a unique limit cycle, which is hyperbolic.

In this paper, we study the coexistence of three types of attractors in an autonomous system in ℝ³: an equilibrium point, a limit cycle and a chaotic attractor. We give an analytical proof of the mechanism for the birth of two different types of these attractors.

By replacing the Chua's diode in Chua's circuit with a first-order hybrid diode circuit, a fourth-order modified Chua's circuit is presented. The circuit has an unstable zero saddle point and two nonzero saddle-foci. By Routh–Hurwitz criterion, it is found that in a narrow parameter region, the two nonzero saddle-foci have a transition from unstable to stable saddle-foci, leading to generations of self-excited and hidden attractors in the modified Chua's circuit simultaneously, which have not been previously reported. Complex dynamical behaviors are investigated both numerically and experimentally. The results indicate that the proposed circuit exhibits complicated nonlinear phenomena including self-excited attractors, coexisting self-excited attractors, hidden attractors, and coexisting hidden attractors.

This paper is concerned with the existence of fast traveling waves connecting an equilibrium and a periodic orbit in a delayed population model with stage structure on a two-dimensional spatial lattice, under the assumption that the corresponding ODEs have heteroclinic orbits connecting an equilibrium point and a periodic solution. In this work, we rewrite the mixed functional differential equation as an integral equation in a Banach space and analyze the corresponding linear operator. Our approach eventually reduces a singular perturbation problem to a regular perturbation problem. The existence of traveling wave solution therefore is obtained by using the Liapunov–Schmidt method and implicit function theorem.

This paper addresses a systematic characterization of saddle-node bifurcations in nonlinear electrical and electronic circuits. Our approach is a circuit-theoretic one, meaning that the bifurcation is analyzed in terms of the devices’ characteristics and the graph-theoretic properties of the digraph underlying the circuit. The analysis is based on a reformulation of independent interest of the saddle-node theorem of Sotomayor for semiexplicit index one differential-algebraic equations (DAEs), which define the natural context to set up nonlinear circuit models. The bifurcation is addressed not only for classical circuits, but also for circuits with memristors. The presence of this device systematically leads to nonisolated equilibria, and in this context the saddle-node bifurcation is shown to yield a bifurcation of manifolds of equilibria; in cases with a single memristor, this phenomenon describes the splitting of a line of equilibria into two, with different stability properties.

By constructing two three-dimensional (3D) rigorous linear systems, a novel switching control approach for generating chaos from two linear systems is presented. Two 3D linear systems without any constant term have only one common equilibrium point that is the origin. By employing an absolute-value switching law, chaos can be generated by switching between two linear systems. Basic dynamical behaviors of the systems are investigated in detail. Numerical examples illustrate the effectiveness of the presented approach.

This paper proposes a novel chaotic system with infinite number of equilibria located on an exponential curve. It signifies an exciting category of dynamical systems which display many features of regular and chaotic motions. The proposed chaotic system belongs to the general category of chaotic systems with hidden attractors. Moreover, some theoretical analyses of the chaotic system’s dynamical characteristics are presented. Using the developed chaotic system, the new random number generator and encryption algorithm have been designed. Encryption application and security analysis are presented verifying its feasibility.