Santosh Kumar Choudhary

This paper presents a mathematical prey-predator model to investigate the intricate, non-linear relationships between phytoplankton, zooplankton, and fish in a marine ecosystem. The model incorporates fundamental ecological processes, including logistic phytoplankton growth, zooplankton grazing on phytoplankton, and fish predation on zooplankton. Additionally, we consider the impact of extreme environmental pressures, including a fear effect, on the marine ecosystem. First, we examine the positivity and boundedness of the proposed model. Furthermore, all the equilibrium points are determined, and the local stability of the system is analyzed around each equilibrium point. The research also explores the impact of rising environmental pressure on population sizes among species. It concludes that greater environmental pressure could drive the system to extinction via a branch point bifurcation. Minimal environmental pressure will destabilize the system via a Hopf bifurcation. We also explore the impact of the fear cost on the zooplankton population and conclude that greater fear costs can cause system instability via another Hopf bifurcation. Theoretical calculations are confirmed by numerical simulations carried out using Mathematica and MATLAB software.

Cancer is the second leading cause of death worldwide and occurs when cells uncontrollably divide, grow, and invade surrounding tissue. Several treatment strategies have been introduced to increase survival rates; however, each approach has potential side effects. Consequently, demand for alternative treatment approaches, such as immune system enhancement with vitamins, is growing. Here, we introduce a mathematical framework based on ordinary differential equations to examine the interactions among nutrients, immune cells, and cancer cells. Unlike many existing tumor–immune models, the proposed framework reveals that variations in nutrient levels can induce qualitative changes in system dynamics, including bistability and regime transitions between tumor-dominant and immune-controlled states. Long-term behavior, stability, and bifurcation techniques are employed. Numerical simulations are performed using the odeint solver in SciPy, which is based on the LSODA algorithm and is capable of handling both stiff and non-stiff systems. Our results suggest that optimizing nutrient levels can enhance the immune response, potentially leading to safer cancer treatment strategies.

One way to strengthen encryption algorithms against attacks is to increase of encryption keys and the level of disorder in the encryption system. This paper investigates a cosine-based memristive model W(φ) = cos(φ) by analyzing the effects of signal amplitude, frequency, and boundary conditions. The proposed memristive element exhibits strong nonlinearity and memory properties, making it suitable for chaotic applications. The memristor is incorporated into a three-cell Hopfield neural network, where it operates as a synaptic coupling element, an external radiation sensor, and a dynamic weight controller. These mechanisms generate rich chaotic dynamics, which are verified using bifurcation diagrams, Lyapunov exponents, and phase space analysis. Numerical simulations in MATLAB are experimentally validated using an ESP32 microcontroller, with chaotic signals observed on an oscilloscope. Based on the proposed Hopfield, an image encryption scheme is developed and evaluated. The encryption results demonstrate high security performance, with entropy of 7.9977, near-zero pixel correlation, NPCR of 99.64%, and PSNR of 6.77. The complete system is practically implemented using an ESP32, a Raspberry Pi, and a computer, confirming its feasibility for real-time secure communication.

This article presents observer-based negative imaginary positive feedback control of satellite orbit dynamical model. In this article, satellite orbital model is transformed into a strongly strict negative imaginary system using observer-based transformation scheme, and then, negative imaginary control theory is applied to achieve stability and robustness in orbit control system in the presence of multiplicative uncertainty. The solutions of orbit control problem are investigated with two thrusters input as well as one thruster input. According to the numerical simulation findings reported in this study, the investigated control approach guarantees the robust stabilization of the satellite orbital system.