Vol. 7, No. 1 (2018): Regular Issue

This paper obtains solutions of the (2+1)-dimensional KadomtsovPetviashivilli-Joseph-Egri equation with power law nonlinearity. This equation is the Joseph-Egri equation formulated in the KP sense. The Lie group analysis and the Exp-function method are used to carry out the integration of this equation. The solutions obtained are solitary waves. Moreover, the conservation laws are constructed by using the multiplier method.

In this manuscript, we study the dynamics of a modified relay-coupled chaotic systems. The modification consists on the fact that the relay unit is modeled to lead the entire network to a desired dynamics. Then we achieve finite-time synchronization indirectly through a linear combination of the three systems. Further, we consider the existence of a switch on time of the coupling from the relay unit to the outer systems. It appears some interesting behaviors such as bifurcations, alternation of crisis and phases transitions when varied the switch on time. An open result is also found. In our scheme and for the selected changeable initial conditions, it seems that the appearance or disappearance of coexistence of attractors is linked to the type of synchronization we are dealing with. Mathematical demonstrations are given to sustain our theory while numerical simulations show its effectiveness.

Reticulated shell structures are usually built as roofs for venues where hundreds or even thousands of people assemble. Failure of this type of structure may endanger the safety of many people. This type of structure can fail due to either material failure or loss of stability (instability). Previous research on structural health monitoring has been focused on the detection of material failure. This study is to timely detect one type of instability in reticulated shell structures, nodal snap-through (NST) instability, to prevent a local NST instability from progressing into an overall structural failure. When an NST instability occurs, a joint and its connected members snap through to their new equilibrium positions, leading the geometric shape in the local area to change significantly. If the displacements at joints are able to be measured, instability can be easily detected from the deformed shape. However, it is very difficult to measure displacements for such large structures located at a high elevation, if not impossible. In this study, an approach to detecting the NST instability will be developed by identifying the change in tilting angles of members, which can be easily measured and essentially reflects the change in geometric shape caused by instability. By applying this approach, a local NST instability can be detected at an early stage, and measures can be taken to prevent a local instability from progressing into a catastrophic structural failure. The effectiveness of this approach has been validated by numerical simulations on a large-scale reticulated shell structure.

The market efficiency theory states that stock returns on efficient markets are random, and then, we cannot predict accurately their future evolutions. Chaos theory is considered as a remedy for this insufficiency since the evolution of chaotic systems appears random but follows precise rules. After the application of detection’s tools of deterministic chaos to IBOVESPA returns, we obtained a fractal dimension equal to 2.5, the convergence of Lyapunov exponent towards positive values and first Lyapunov exponent characterized by its positivity. Results obtained after the application of the Nearest Neighbors method allows us to conclude IBOVESPA returns are characterized by sensitivity to initial conditions and are therefore chaotic.

This paper deals with the numerical computations for the controllability of linear and nonlinear composite fractional dynamical systems. The goal is to compute a control state that drives the system from a prescribed initial state to described final state in a large enough controllability time. We address the controllability results using Grammian matrix and iterative technique. Some examples are provided to illustrate the results.

This note considers the work entitled “Unknown Input Observer Design for Linear Fractional-Order Time-Delay Systems”. In the above paper [1], the authors gave the existence conditions of such observer, then based on the fractional order Lyapunov stability approach, a sufficient condition for the asymptotic stability of the estimation error have given in a linear matrix inequality (LMI) formulation which is incorrect. In this note, we give the correction of Theorem 7. The new proposed Theorem can be applied to a large kind of delayed fractional-order-system when the delay is time varying or constant, while the above mentioned paper consider only a constant time delay. The proof is based on the diffusive representation of the fractionalorder derivative and the indirect Lyapunov approach proposed in [2].

The adult skeleton is a highly specialised organ that undergoes constant remodelling over time. Bone metastasis affect the dynamic of this process. For this reason, the study of this dynamic model is essential to the development of better therapies for the disease. Anomalous diffusion phenomena are often found in biological systems, and can be modelled using fractional order derivatives. Consequently, this paper modifies models presented in the literature, consisting of differential equations of order one, checking how their behaviour changes when fractional derivatives are used instead. Results for both local and one-dimensional models of healthy bone tissue and of tumourous bone tissue have the characteristics expected from the literature, with higher fractional orders leading to a faster, more oscillatory system whereas lower orders have a more damped behaviour.

This paper is a continuation of our previous studies on nonlinear consensus. We have considered a nonlinear protocol for a structured time-invariant and synchronous multi-agent system. We present an opinion sharing dynamics of the multi-agent system as a trajectory of a polynomial stochastic operator associated with a stochastic multidimensional hyper-matrix. We provide a criterion for a uniform consensus in the multi-agent system. Particularly, the uniform consensus is achieved in the multi-agent system if all entries of the stochastic multidimensional hyper-matrix are positive. Some numerical results are also presented to support our theoretical results.

Dynamics of chains of three and four coupled non-identical Josephson junctions is considered. Synchronization effects are discussed including resonance Arnold web formation on the base of tori of different dimensions.