It was observed that the spatiotemporal chaos in lattices of coupled chaotic maps was suppressed to a spatiotemporal fixed point when some fractions of the regular coupling connections were replaced by random links. Here we investigate the effects of different kinds of parametric fluctuations on the robustness of this spatiotemporal fixed point regime. In particular we study the spatiotemporal dynamics of the network with noisy interaction parameters, namely fluctuating fraction of random links and fluctuating coupling strengths. We consider three types of fluctuations: (i) noisy in time, but homogeneous in space; (ii) noisy in space, but fixed in time; (iii) noisy in both space and time. We find that the effect of different kinds of parametric noise on the dynamics is quite distinct: quenched spatial fluctuations are the most detrimental to spatiotemporal regularity; patiotemporal fluctuations yield phenomena similar to that observed when parameters are held constant at the mean value, and interestingly, spatiotemporal regularity is most robust under spatially uniform temporal fluctuations, which in fact yields a larger fixed point range than that obtained under constant mean-value parameters.

Many natural and engineered complex networks have intricate mesoscopic organization, e.g., the clustering of the constituent nodes into several communities or modules. Often, such modularity is manifested at several different hierarchical levels, where the clusters defined at one level appear as elementary entities at the next higher level. Using a simple model of a hierarchical modular network, we show that such a topological structure gives rise to characteristic time-scale separation between dynamics occurring at different levels of the hierarchy. This generalizes our earlier result for simple modular networks, where fast intramodular and slow intermodular processes were clearly distinguished. Investigating the process of synchronization of oscillators in a hierarchical modular network, we show the existence of as many distinct time-scales as there are hierarchical levels in the system. This suggests a possible functional role of such mesoscopic organization principle in natural systems, viz., in the dynamical separation of events occurring at different spatial scales.

This paper presents a new scheme for constructing bidirectional nonlinear coupled chaotic systems which synchronize projectively. Conditions necessary for projective synchronization (PS) of two bidirectionally coupled chaotic systems are derived using Lyapunov stability theory. The proposed PS scheme is discussed by taking as examples the so-called unified chaotic model, the Lorenz–Stenflo system and the nonautonomous chaotic Van der Pol oscillator. Numerical simulation results are presented to show the efficiency of the proposed synchronization scheme.

We consider a model for insect–pathogen interaction where the insect population is divided into two groups, one group susceptible to disease and other resistant to disease. An individual born susceptible to or resistant to disease depends on the local population levels at the start of each generation. Here we consider density-dependent models of transmission because we characterize diseases that spread through environmental propagules or through random contact among individuals. We consider the case where the fraction of resistant individuals increases as the total population increases. White and Wilson (Theor. Popul. Biol. 56, 163 (1999)) have reported the results of density-dependent monotonic increase of resistance class by choosing a particular type of function. In this paper, we have chosen a class of monotonic density-dependent resistance functions and studied their effects on insect–pathogen dynamics. In particular, we have investigated the effects of different types of monotonic density-dependent resistance on the bistable nature of the model. Numerical simulation results are presented and interpreted.

In this communication, different classes of phenomenological universalities of carrying capacity dependent growth processes have been proposed. The logistic as well as carrying capacity-dependent West-type allometry-based biological growths can be explained in this proposed framework. It is shown that logistic and carrying capacity-dependent West-type growths are phenomenologically identical in nature. However, there is a difference between them in terms of coefficients involved in the phenomenological descriptions. Involuted Gompertz function, used to describe biological growth processes undergoing atrophy or a demographic and economic system undergoing involution or regression, can be addressed in this proposed environment-dependent description. It is also found phenomenologically that the energy intake of an organism depends on carrying capacity whereas metabolic cost does not depend on carrying capacity. In addition, some other phenomenologicaldescriptions have been examined in this proposed framework and graphical representations of variation of different parameters involved in the description are executed.

Many researchers introduce schemes for designing multistable systems by coupling two identical systems. In this paper, we introduce a generalized scheme for designing multistable systems by coupling two different dynamical systems. The basic idea of the scheme is to design partial synchronization of states betweenthe coupled systems and finding some completely initial condition-dependent constants of motion. In our scheme, we synchronize $i$ number $(1 \leq i \leq m − 1)$ of state variables completely and keep constant difference between $j$ $(1 \leq j \leq m −1, i + j = m)$ number of state variables of two coupled m-dimensional different dynamical systems to obtain multistable behaviour.We illustrate our scheme for coupled Lorenz and Lu systems. Numerical simulation results consisting of phase diagram, bifurcation diagram and maximum Lyapunov exponents are presented to show the effectiveness of our scheme.

In this paper, the classical problem of the motion of a particle in one dimension with an external time dependent field is studied from the point of view of the dynamical system. The dynamical equations of motion of the particle are formulated. Equilibrium points of the non-oscillating systems are found and their local stability natures are analysed. Effect of oscillating potential barrier is analysed through numerical simulations. Phase diagrams,bifurcation diagrams and variations of largest Lyapunov exponents are presented to show the existence of a wide range of nonlinear phenomena such as limit cycle, quasiperiodic and chaotic oscillations in the system. Effects ofnonlinear damping in the model are also reported. Analysis of the physically interesting cases where damping is proportional to higher powers of velocity are presented for the sake of generalizing our findings and establishingfirm conclusion.

Multistability or coexistence of different chaotic attractors for a given set of parameters depending on the initial condition only is one of the most exciting phenomenon in dynamical systems. The schemes to designmultistability systems via coupling two identical or non-identical but the same-dimensional systems have been proposed earlier. Coupled different-dimensional systems are very useful to describe the real-world physical and biological systems. In this paper, a scheme for designing a multistable system by coupling two different-dimensional dynamical systems has been proposed. Coupled Lorenz and Lorenz–Stenflo systems have been considered to illustrate the scheme. The efficiency of the scheme is shown numerically, by presenting phase diagrams, bifurcation diagrams and variation of maximum Lyapunov exponents.

A rule for designing extreme multistable synchronised systems by coupling two identical dynamical systems has been proposed in this paper. The basic idea behind the proposed scheme is the existence of chaos in the coupled system in the presence of initial condition-dependent constants of motion. A new conjecture has been introduced according to which an extreme multistable synchronised system can be designed if all states of one system will synchronise with the corresponding states of the other system (of the two coupled systems) and the basin of the synchronised state depends on the difference between the initial conditions of the corresponding states of the individual systems. The proposed scheme has been illustrated with the help of coupled Rössler systems, coupled Hénon maps and coupled logistic maps. Moreover, the existence of flip bifurcation with the variation of initial conditions has been shown analytically as well as numerically in the case of coupled Hénon maps. Numerical results are reported to show the proficiency of the proposed scheme to design extreme multistable synchronisation behaviour. This work establishes a theoretical foundation for constructing extreme multistable synchronised continuous as well as discrete dynamical systems.