Vol. 14, No. 3 (2025): Regular Issue

The fact that the Earth is becoming hotter poses an existential threat for some life forms on Earth. But what is heat? Surprisingly, the answer to this question is not completely clear. We here explore the history of the quest to understand the microscopic mechanical origins of heat. We also describe what is presently known about the dynamical structure of phase space when heat is present.

This article studies the formation control problem of multiple unmanned aerial vehicles systems (UAVs) against denial-of-service (DoS) attacks. During the data transmission process, malicious attackers try to block the data transmission path through DoS attacks, which may result in the leader information being unavailable. To address this issue, the distributed formation observer is introduced. Considering that regular formation errors may become non-differentiable when systems are subject to DoS attacks, which makes it impossible to implement the backstepping control methodology, this article formulates a new tracking error based on the distributed formation observer to overcome this difficulty. Due to the existence of uncertain nonlinear functions in multiple UAVs, fuzzy logic systems (FLSs) have been employed to approximate these uncertain terms. Subsequently, the distributed observer-based fuzzy adaptive formation controller is proposed by utilizing the backstepping control methodology, making multiple UAVs resilient to DoS attacks. Finally, simulation results indicate the effectiveness of the presented fuzzy adaptive formation control scheme.

This paper discusses the optimal attitude synchronization of quadrotor unmanned aerial vehicles with full-state constraints. First, a distributed observer is constructed to generate a reference trajectory for each QUAV. Then, a global unified barrier function is constructed to transform the constrained control problem into an unconstrained one. By ensuring that the states of the transformed system are bounded, the states trajectory of the QUAV are always within the constrained range. Considering the uncertainty of QUAVs model, a model-free reinforcement learning algorithm is designed to obtain the optimal attitude control law. Finally, the effectiveness of the proposed control strategy is verified by simulation experiments. The simulation results show that the proposed method can effectively realize the optimal formation without state transgression.

We study the motion of a test particle in a conservative force field. We find three-dimensional and planar potentials producing a pre-defined two-parametric family of spatial orbits given in the solved form $f(x,y,z)$=$c_{1}$, $g(x,y,z)$=$c_{2}$ which can be represented by a pair of functions $\alpha(x,y,z)$ and $\beta(x,y,z)$ uniquely. We apply a new methodology in order to find potentials depending on the orbital functions $\alpha(x,y,z)$ and $\beta(x,y,z)$ , i.e., potentials of the form $V(x,y,z)=F(w(\alpha, \; \beta))$ where $w$ is an specific combination of the pair ($\alpha, \; \beta$). For an appropriate pair ($\alpha, \; \beta$), we find homogeneous potentials of zero degree, axially symmetric potentials and other results. Moreover, we focus our interest on 2D potentials such as Newtonian, cored, logarithmic and quartic potentials which have many astronomical applications. Families of straight lines are also examined.

The solution of a set of non-linear differential equations applying Adomian Decomposition Method (ADM) provides fast computation for the solution. The main part of this method is calculating Adomian polynomials with respect to nonlinear terms. Here, we analyze an ecosystem with one prey and two predator species. The functional response among the species is taken as ratio dependent. We have discussed local stability analysis of our proposed model around different equilibrium points. We have found out the approximate series solution of our proposed system using Adomian decomposition method. We have presented some graphical examples to show the ability of ADM for a nonlinear set of differential equations.

In this paper, we investigate the relationship between the dynamics of bank loans and several central bank policies, including reserve requirement, capital adequacy ratio, and deposit and loan benchmark interest rates. Using bifurcation analysis, we investigate the effect of loan stability on the policies resulting in transcritical and flip bifurcations. We validate the analytical results by presenting a one-parameter bifurcation diagram to see the impact of each policy and a two-parameter bifurcation diagram to examine the impact of the combination of two central bank policies on loan stability. In addition, we present a sensitivity analysis of the effect of the combination of two policies using a contour plot.

Mathematical models have significantly contributed by showing how virological synapses are created to enable cell-to-cell transmission. To replicate the crowding effect of Human Immunodeficiency Virus (HIV), this study, motivated by previous studies, attempts to develop a new compartmental epidemic model with two delays and nonlinear incidence rates. The first delay occurs between the time the virus enters the body and the beginning of HIV latency. The second delay occurs when infected cells must produce virions. We thoroughly investigated the local stability of the model's stable states using the delay differential equation stability theory and calculated the basic reproductive number ($R_0$). Numerical simulations were also conducted to assess the relative contributions of the two delayed viral transmission modes, investigate the effects of time delays and other factors on disease dynamics, and assess the effects of time delays on disease dynamics. We used the Partial Rank Correlation Coefficient (PRCC) to do a global sensitivity analysis and identify the most sensitive parameters affecting $R_0$, providing information on potential ways to slow down the progression of the HIV disease. We offered an extensive numerical analysis for our deterministic and delay models, including bifurcations and time series. Our simulation indicates that to keep the system predictable, we should control the time delay, $\tau_1$, which stands for the interval between viral entry into an uninfected target cell and the generation of an active target cell. In addition to outlining basic management measures, the current study demonstrates the complex dynamics of two delayed HIV models.

Robotic fish have evolved to accomplish numerous inaccessible tasks and investigations in unreachable aquatic environments. Recently, the increasing interest in underwater exploration motivates the development of aquatic unmanned vehicles. Biomimetic robots have been developed by researchers based on the different parameters including maneuverability, cruising speed, and propulsion efficiency. This paper presents a design of torpedo-like fish robot with the required dynamics and hydrodynamics performance characteristics through Computational Fluid Dynamic application (SolidWorks Flow Simulation). The suggested model is built with a torpedo-shape to reduce drag forces while increasing thrust. The robot is propelled by a propeller fan with different number of blades (i.e., 2, 3, 4 and 5 blades). The propeller is actuated by a dc motor with (0 to 100 RPM). The required dynamics like motor torque, power consumption and angular velocities were calculated and compared with the hand calculations to validate our design.

In this study, we first design an eco-epidemiological model in the presence of a contagious disease in prey population. Prey population following logistic law of growth is classified into two groups: susceptible and infected. The impacts of anti-predatory behaviour for the fear effects of predators are duly investigated. Assumptions are made that the fear effects are capable of reducing prey reproduction rate and alleviating disease transmission rate by lowering prey activity. Additionally, we consider Allee effects, wherein the growth rate of the susceptible prey population is diminished by the fear effects. Hunting cooperation of predator is also incorporated in the proposed model. The model is then transformed into a delayed eco-epidemiological model by accounting for gestation time required to reproduce a new member of the predator family. Equilibrium points and corresponding existence criteria are calculated, and local behaviours of the non-delayed model are analyzed. The delayed model is examined for Hopf bifurcation with time delay as a bifurcating parameter. All the probable directions and the stability of bifurcating periodic solutions are also studied. The effects of herd behaviour, fear, Allee effects, hunting cooperation, and other biological parameters are demonstrated through extensive numerical simulations. Meanwhile, we uncover that predators can control the spread of the disease within the prey population until a certain threshold in the disease transmission rate. They achieve this by consuming infected individuals from the ecosystem. Beyond direct participation, predator also crucially contribute to disease control through fear. Their presence separates strong prey from infected individuals, minimizing the likelihood of direct contact.

The double coplanar pendulum is an example of the coexistence of regular and chaotic dynamics for equal energy values but different initial conditions. Regular trajectories predominate for low energies; as the energy is increased, the system passes through values where chaotic trajectories are abundant, and then, increasing the energy further, it is again dominated by regular trajectories. Given that the energetically accessible states are bounded, a relevant question is about the fraction of phase space regular or chaotic trajectories as the energy varies. In this paper, we calculate the relative abundance of chaotic trajectories in phase space, characterizing the trajectories using the maximum Lyapunov exponent, and find that, for low energies, it grows exponentially.

In current study, nonlinear vibration and frequency response analysis of double walled piezoelectric nanoresonator (DWPENR), simultaneously subjected to visco-Pasternak medium, nonlinear van der Waals force and electrostatic excitation is investigated using the Gurtin--Murdoch surface/interface (S/I) and nonlocal theories. For this analysis, Hamilton's principle is used to obtain the governing equations and boundary conditions and Galerkin technique is used to solve the equation of motion. Complex averaging method combined with arc-length continuation is used to achieve the influences of the small-scale, surface effects, elastic medium, van der Waals force, electrostatic and piezoelectric voltages and other parameters on dimensionless natural frequency (DNF), nonlinear frequency response and stability analysis of the DW piezoelectric nanoresonator. It is concluded that ignoring surface and small-scale effects lead to inaccurate results in vibrational response of the DWPENR. It is found that with increasing or decreasing of dimensionless nonlocal parameter and surface/interface parameters, due to increasing or decreasing of DWPENR stiffness, lead to increasing or decreasing DNF, the resonance amplitude and frequency, the range of instability with saddle-node bifurcations and nonlinear softening or hardening behavior and all nonlinear behavior of DWPENR. The obtained results of this study may be useful for designing of nano/micro electro mechanical system and other nano-/micro-smart structures.

Vigilance is an anti-predator behavior that creates a trade-off between foraging and safety, impacting the growth rate of prey. In this work, we study the dynamics of a predator-prey system where the prey exhibit active vigilance in the presence of predators. Vigilance behavior reduces predation risk and can lead to a competition for resources (prey) among predators. We provide conditions for the feasibility and local stability of equilibrium points as well as global stability results for the system. We demonstrate the possible occurrence of saddle-node and Hopf bifurcations when varying the parameters for the level of vigilance $v$ and predator intraspecific competition $c$. Additionally, we numerically show the possible occurrence of cusp and Bogdanov-Takens bifurcations. Our results indicate that increased vigilance leads to a reduction in prey growth rate and highlight that prey vigilance and predator intraspecific competition play a key role in maintaining ecosystem stability. We also extend our system to include a spatial component, observing the occurrence of spatial Turing patterns in one and two dimensions. We present numerical experiments to support our findings and discuss the applications of our results in species conservation and pest control.

A new simple 6D hyperchaotic system (high dimension) with four positive ($4+ve$) Lyapunov exponents (LEs) is constructed via coupling between a 1D nonlinear system and a 5D system. The proposed system is considered simple because it consists of thirteen terms only, two of which are quadratic nonlinearly with two coupling parameters. This 6D system has two unstable equilibria points and belongs to the self-excited attractors. This system exhibits the highest Lyapunov exponents and Kaplan-Yorke dimension compared to the 13 other 6D systems in existing literature. The new system's dynamical analysis is investigated theoretically and numerically, including equilibria points, divergence, Lyapunov exponents, Lyapunov dimension, phase portrait, coexisting attractors, and electronic circuit. Thereafter, complete synchronization (CS) between two identical 6D systems had been achieved.

In this work, we propose a ratio-dependent intraguild predation model that incorporates fear and gestation delay. Further, the cost of the intraguild predator's fear is thought to decrease the size of the intraguild prey. The interaction between prey and predator takes place in the form ratio-dependence type. This type of functional response offers a valuable perspective by considering the feeding rates based on the relative abundance of both prey and predators. We first determine the conditions under which positive equilibrium points exist, and then we examine the local stability properties of the equilibria. In order to gain insight into the rich dynamics of the proposed non-delayed model, the occurrence of Hopf-bifurcation with respect to the fear parameter near the interior equilibrium point is discussed. Furthermore, we evaluate the local stability and the possibility of a Hopf bifurcation for the delayed model. The direction and stability of the Hopf bifurcation are also studied using the center manifold theorem. Finally, we conduct the numerical simulations to demonstrate our analytical results.

Dengue infection primarily occurs in tropical and subtropical regions. Climate change exacerbates the transmission of dengue fever. Therefore, stochastic modeling is significantly more efficient than a deterministic model. In this context, we work with deterministic and stochastic differential equation models. We have calculated the basic reproduction number ($R_0$) at the point when the disease-free equilibrium state is stable. The progression of the infection is contingent upon the value of $R_0$, and the disease can be effectively managed when $R_0$ is less than 1. Furthermore, the presence of the disease becomes apparent when the basic reproduction number ($R_0$) exceeds 1. This study enhances our comprehension of the transfer of infection between human hosts and mosquito vectors. In order to analyze the stochastic model, we employ the Euler-Maruyama and stochastic Runge-Kutta techniques. Additionally, we present the stochastic nonstandard finite difference scheme (SNSFD), which maintains the model's fundamental features, such as positivity, boundedness, and dynamic consistency, regardless of the chosen step size. The numerical results obtained from our stochastic model provide support for the validity of the stochastic differential equation model and its analytical findings.