Debabrata Biswas

We report the experimental realization of minimal chimera states in a system of three uncoupled oscillators driven solely by frequency-modulated forcing. Unlike conventional scenarios where chimera states emerge due to interactions among oscillators, here the coexistence of coherent and incoherent dynamics arises entirely from a common external modulation of a system parameter. By tuning the modulation amplitude and frequency, the system exhibits transitions between global synchronization, global incoherence, and minimal chimera states. The stability of these regimes is quantified using the maximal Lyapunov exponent, while a synchronization order parameter is employed to characterize the degree of coherence. A systematic exploration of the parameter space reveals well-defined regions associated with distinct dynamical behaviors. To provide analytical understanding, we employ a phase-reduction approach and derive the corresponding phase dynamics, which elucidate the mechanisms underlying phase locking and desynchronization. The robustness of the proposed mechanism is further demonstrated in a time-delayed chaotic system. Finally, experimental results obtained from an electronic circuit realization confirm the emergence of minimal chimera states under frequency-modulated driving. These findings establish external modulation as a viable route to chimera formation without coupling, offering a unique perspective on collective dynamics in driven nonlinear systems.

In this paper, we explore the features of a genetic network where the transcription factors, namely, activators and repressors bind to the promoter in a competitive way. We have developed an analytical method to find the most probable set of parameter values that are unavailable in experiments. We study the behavior of intrinsic noise of the circuit and compare the profile with the network where the activator and the repressor bind the promoter noncompetitively. We observe that the noise found in the super-Poissonian region of the competitive genetic circuit is higher than the noise obtained in the same from a noncompetitive one. We further notice that, due to the effect of transcriptional reinitiation in the presence of the activator and repressor molecules, there exist some anomalous characteristic features in the mean expressions and noise profiles. On top of that, we find low noise in the transcriptional level and high noise in the translational level in presence of reinitiation than in absence of the same. In addition, we find out the method to reduce the noise further below the Poissonian level in competitive circuit than the noncompetitive one with the help of some noise-reducing factors. We also notice that the effect of extrinsic noise due to the environmental fluctuation on the competitive activator-repressor system is insignificant in the low noise limit.

We present a comprehensive study of a tumor-immune interaction model with delayed immune activation, combining analytical, numerical, and experimental approaches. A central feature of our formulation is the use of a generalized Hill function for immune activation, where the exponent m introduces tunable cooperativity. This generalization extends beyond conventional Michaelis–Menten or fixed-saturation forms and captures a wider range of nonlinear immune responses. On the analytical side, we derive explicit conditions for transcritical and Hopf bifurcations, clarifying the roles of key biological parameters and the immune response delay in shaping tumor dynamics. Numerically, we investigate the time-series, phase-plane plots, and both single- and two-parameter bifurcation scenarios with respect to the delay and other system parameters that confirmed the observed transitions are in excellent agreement with the analytical predictions. Most importantly, we implement the delayed tumor-immune model in an analog electronic circuit by reformulating the Hill activation function in terms of hyperbolic tangents, enabling direct laboratory exploration of the system. Experimental investigations reveal steady-state and oscillatory behaviors, dependent on time delay, that closely match the numerical simulations, despite the unavoidable real-world effects such as parameter mismatch, noise, and fluctuations. To the best of our knowledge, this is the first realization of a time-delayed tumor-immune model in hardware in the physics laboratory. This provides a novel bridge between mathematical theory, numerical analysis, and experimental validation and opens new directions for probing tumor dormancy, immune oscillations, and relapse under controlled physical conditions.

Birhythmicity is evident in many nonlinear systems, which include physical and biological systems. In some living systems, birhythmicity is necessary for response to the varying environment while unnecessary in some physical systems as it limits their efficiency. Therefore, its control is an important area of research. This paper proposes a space-dependent intermittent control scheme capable of controlling birhythmicity in various dynamical systems. We apply the proposed control scheme in five nonlinear systems from diverse branches of natural science and demonstrate that the scheme is efficient enough to control the birhythmic oscillations in all the systems. We derive the analytical condition for controlling birhythmicity by applying harmonic decomposition and energy balance methods in a birhythmic van der Pol oscillator. Further, the efficacy of the control scheme is investigated through numerical and bifurcation analyses in a wide parameter space. Since the proposed control scheme is general and efficient, it may be employed to control birhythmicity in several dynamical systems.

Network structure or connectivity patterns are critical in determining collective dynamics among interacting species in ecosystems. Conventional research on species persistence in spatial populations has focused on static network structure, though most real network structures change in time, forming time-varying networks. This raises the question, in metacommunities, how does the pattern of synchrony vary with temporal evolution in the network structure. The synchronous dynamics among species are known to reduce metacommunity persistence. Here we consider a time-varying metacommunity small-world network consisting of a chaotic three-species food chain oscillator in each patch or node. The rate of change in the network connectivity is determined by the natural frequency or its subharmonics of the constituent oscillator to allow sufficient time for the evolution of species in between successive rewirings. We find that over a range of coupling strengths and rewiring periods, even higher rewiring probabilities drive a network from asynchrony towards synchrony. Moreover, in networks with a small rewiring period, an increase in average degree (more connected networks) pushes the asynchronous dynamics to synchrony. On the other hand, in networks with a low average degree, a higher rewiring period drives the synchronous dynamics to asynchrony resulting in increased species persistence. Our results also follow the calculation of synchronization time and are robust across other ecosystem models. Overall, our study opens the possibility of developing temporal connectivity strategies to increase species persistence in ecological networks.